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A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Disjoint Packing

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Pith's one-line read The paper introduces non-half-sum disjoint packing, a combinatorial condition that unifies placement and delivery, and uses it to build coded caching schemes with subpacketization equal to the number of users and lower transmission load…

desk verdict A genuinely new combinatorial framework with a correct core construction, but the paper overclaims its comparisons and includes a wrong formula in an appendix. read the letter →

arxiv 2501.11855 v3 pith:KXYMXNVK submitted 2025-01-21 cs.IT math.IT

Minquan Cheng , Huimei Wei , Kai Wan , Giuseppe Caire This is my paper · ORCID
classification cs.ITmath.IT MSC 94A1505B30
keywords codedcachinglinearsubpacketizationplacementdeliveryarraytransmissionloadnon-half-sumdisjointpackingcyclicdifferencenon-three-termarithmeticprogressionperfecthashfamily
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Fixing the number of users $K$ and the cache-to-file ratio, coded caching's two practical bottlenecks are the transmission load $R$ and the subpacketization $F$, the number of pieces each file is cut into. Most low-load schemes force $F$ to grow exponentially with $K$; the few known schemes with $F$ linear in $K$ pay for it with large $R$. This paper claims a middle path: a new combinatorial object, the non-half-sum disjoint packing (NHSDP), turns a $v\times v$ Latin square into a placement-delivery array with $K=F=v$, gain equal to the block size, and load equal to the number of blocks. The authors construct NHSDPs explicitly and report that the resulting schemes beat all existing linear-subpacketization schemes in load, beat some polynomial-subpacketization schemes, and approach exponential-subpacketization performance. If correct, the paper establishes a single design principle that simultaneously handles placement and delivery and yields practical schemes with linear subpacketization.

What carries the argument

Non-half-sum disjoint packing (NHSDP): for odd $v$, a collection $\mathcal{D}$ of $b$ disjoint $g$-subsets of $\mathbb{Z}_v$ such that the half-sum $(x+y)/2$ of any two distinct elements of any block never appears in any block. It carries the argument because it integrates placement and delivery: the blocks determine where a Latin-square array is filled with integers, and the half-sum condition determines where the stars must sit, so a single definition supplies both the cache layout and the guarantee that every transmitted XOR reaches its intended users.

What would settle it

For Construction 2 with $m_1=m_2=m_3=2$, take the odd value $v=123$, below $2\phi+1=125$: the element $-62$ generated by block $a=(2,2,2)$ equals $61$ modulo $123$, and $61$ is generated by block $a=(1,2,2)$, so block disjointness fails. Checking all odd $v\ge125$ for the same parameters would confirm the claimed validity region.

Watch

Extended reading notes

Core claim

The paper's central claim is Theorem 1: from any $(v,g,b)$ NHSDP, Construction 1 produces a $(v,v,v-bg,bv)$ placement-delivery array, hence a $(K=v,M,N)$ coded caching scheme with $K=F=v$, memory ratio $M/N=1-bg/v$, coded caching gain $g$, and transmission load $R=b$. The construction places the difference $k-f$ of a Latin-square entry into one of $b$ disjoint $g$-subsets of $\mathbb{Z}_v$; the NHSDP's second condition, that no half-sum of two elements of a block lies in any block, is exactly what forces the XOR deliveries to be decodable. With the explicit family of Construction 2, built from coordinate weights $x_i$ satisfying $x_{i+1}>2\sum_{j\le i}f(j)$, the paper obtains $v\ge2\phi(m_1,\ldots,m_n)+1$, gain $2^n$, load $\prod_i m_i$, and subpacketization $v$, with the balanced choice $m_i=\lfloor(v^{1/n}-1)/2\rfloor$ giving load $\lfloor(v^{1/n}-1)/2\rfloor^n$. The authors argue numerically and theoretically that these schemes beat the known linear-subpacketization schemes in load and are competitive with schemes using much larger subpacketization.

Load-bearing premise

The construction's correctness rests on the coordinate weights in Construction 2 growing fast enough that no two block representations coincide in $\mathbb{Z}_v$ and no half-sum of a block reappears in any block; this requires $v$ odd and $v\ge2\phi+1$, and it collapses if $v$ is chosen smaller so that wrap-around identifies two distinct integers.

Editorial extensions

If this is right

  • For every choice of $n$ and $m_1,\ldots,m_n$ with $v\ge2\phi+1$, the constructed scheme has $K=F=v$, gain $2^n$, and load $\prod_i m_i$, so the designer can trade memory and load across many operating points.
  • At the balanced point $m_i=\lfloor(q-1)/2\rfloor$ with $q=v^{1/n}$, the scheme matches the memory ratio of the MN scheme while reducing subpacketization by a factor exponential in $K$, at a modest load increase.
  • Compared with the WCWL, ZCW, AST, and XXGL linear-subpacketization schemes, the proposed scheme achieves smaller or equal subpacketization and lower load in the parameter ranges the paper tabulates.
  • The conjugate PDA of the balanced construction gives a high-memory regime with memory ratio $1-(2/q)^n$ and load $\lfloor(q-1)/2\rfloor^{-n}$, extending the same design to memory ratios near 1.
  • When $q=3$, the construction yields an NTAP set of size $2^n$ in $\mathbb{Z}_{3^n}$, improving the known generic lower bound on maximal NTAP size for $n\le52$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The NHSDP condition is not tied to the specific Latin square $f+k$; the same half-sum argument would work for any Cayley table of an abelian group of odd order, so other group tables might yield NHSDP families with different parameters.
  • The explicit NTAP sets obtained at $q=3$ suggest a constructive route to better bounds on the maximum NTAP size for intermediate $v$, not just powers of 3, by interpolating the coordinate-weight construction.
  • Solving the integer program in Problem 1 exactly rather than through the symmetric relaxation could produce schemes with lower memory ratio at fixed gain, since the paper's closed form is only shown optimal when $q$ is an odd integer.
  • A natural testable extension is to allow block sizes other than $2^n$, for example by using higher-dimensional coefficient sets or mixed radices, which the paper lists as future work.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper introduces a new combinatorial object, the non-half-sum disjoint packing (NHSDP), and shows that a (v,g,b) NHSDP yields a (v,v,v-bg,bv) placement-delivery array via Construction 1, hence a coded caching scheme with linear subpacketization F=v, memory ratio M/N=1-bg/v, gain g, and load R=b (Theorem 1). It then constructs explicit NHSDPs in Construction 2 by embedding blocks as signed sums of dominating coordinate weights; Lemma 3 proves that this yields a (v,2^n,prod m_i) NHSDP whenever v is odd and v >= 2*phi(m_1,...,m_n)+1. This gives schemes with K=v, F=v, gain 2^n, load prod m_i (Theorem 2), and the optimization in Theorem 3 selects m_i = floor((v^{1/n}-1)/2), producing load close to floor((v^{1/n}-1)/2)^n. The paper compares these schemes with several existing linear-, polynomial-, and exponential-subpacketization schemes and connects NHSDP to cyclic difference packings, non-three-term arithmetic progressions, and perfect hash families.

Significance. If the results are correct after revision, the NHSDP framework is a valuable unifying condition for linear-subpacketization coded caching: it integrates placement and delivery into a single condition, and the explicit Construction 2 family achieves load roughly (v^{1/n}/2)^n while keeping F=K, which is competitive with or better than several prior schemes in the linear-subpacketization regime. The connections to NTAP and PHF also give new explicit objects, including an NTAP lower bound that beats the previous bound for small n and PHFs with more columns than the quadrics construction. The main proofs are self-contained and the key PDA verification in Theorem 1 is sound. The paper's abstract claim of lower load than all existing linear-subpacketization schemes is not yet supported because the MR scheme [29] is omitted from the comparisons, and the proof of Theorem 3 contains a false formula in Eq. (25); these issues are local and fixable, so the underlying framework remains promising.

major comments (2)
  1. [Appendix C, Eq. (25); Remark 2] Equation (25) states that when q=v^{1/n} is an odd integer, the blocks are D_a = {sum_i alpha_i a_i q^{i-1} | alpha_i in {-1,1}} for all a in [q]^n. This is inconsistent with Construction 2 and Lemma 3, where the block indices are restricted to A=[m_1] x ... x [m_n] and in Theorem 3 m_i=(q-1)/2. For q=5, n=2, the block D_{(1,1)} under (25) contains 4 and 6, whose half-sum 5 equals -5+10 and hence appears in D_{(5,2)} under the [q]^n range, violating Definition 2. It also contradicts the block count b=m^n: with [q]^n there would be q^n blocks, not ((q-1)/2)^n. Since the proof of Theorem 3 and Remark 2 rely on this formula, the proof as written is internally inconsistent. Replace [q]^n with [((q-1)/2)]^n, i.e., use (9) directly with m_i=(q-1)/2; the claimed family is then consistent with Lemma 3.
  2. [Section V-A and Abstract claim (i)] The headline claim that the proposed scheme achieves a lower load than existing schemes with linear subpacketization is not fully supported, because the theoretical and numerical comparisons omit the MR scheme [29], which is listed in Table I and has linear subpacketization F=K. The phrase in Section V-A that only [16], [20], [24], [26], [27] have special parameters does not justify excluding [29]. To substantiate claim (i), the authors should compare with [29] (and ideally with [30]) for the same K and comparable memory ratios, or explicitly restrict the claim to the schemes actually compared.
minor comments (4)
  1. [Remark 2] There is a typo: "cachign" should be "caching".
  2. [Lemma 4] The lemma statement begins "Gvien a ... PDA", which should be "Given a ... PDA".
  3. [Appendix A] In the proof of Theorem 1, "This contracts the condition of NHSDP" should read "This contradicts the condition of NHSDP".
  4. [Lemma 6] The set is written as "D = {alpha_1 + 3 alpha_2 + ... + 3^{n-1} alpha_n | alpha_i in {-1,1}}"; please make explicit that this is the single block D_{(1,...,1)} in Z_{3^n} and that the half-sum condition is verified over that ring.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NHSDP-to-PDA and Construction-2-to-NHSDP derivations are self-contained; self-citations are background only.

full rationale

The core derivation chain is not circular. Theorem 1's proof in Appendix A starts from the two NHSDP conditions and derives the PDA parameters by direct counting: disjointness gives Z = v - bg, the Latin-square construction gives the Latin property, and the half-sum exclusion gives the C3-b corner-star property, yielding the (v, v, v - bg, bv) PDA without assuming the conclusion. Lemma 3's proof in Appendix B independently establishes disjointness and half-sum exclusion from the dominance inequality x_{i+1} > 2 sum_{j<=i} f(j) and the wrap-around bound v >= 2phi + 1; no fitted parameter is renamed as a prediction. The comparisons with existing schemes are against published external designs. The self-citations to the PDA framework (Lemmas 1-2 from [8], [9]) and the conjugate-PDA lemma from [11] are standard background results and are not load-bearing for the new NHSDP construction. I note for completeness that the Appendix C formula in Eq. (25), which indexes blocks by a in [q]^n when q is odd, is internally inconsistent with Construction 2 and Lemma 3, which require a in [(q-1)/2]^n; this is a correctness bug in the proof as written, not a circular reduction of the claimed result to its inputs.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The construction depends on the standard PDA model, on odd v for invertibility of 2, and on standard convex optimization. No parameters are fitted to data, and no new physical entities are postulated. The m_i are design variables chosen in closed form by Theorem 3, not fitted constants.

assumptions (3)
  • domain assumption Odd v is required so that 1/2 is invertible in Z_v (Definition 2 and Theorem 1).
    The half-sum operation and the unique solution of k+f=c, k-f=d both require division by 2 modulo v; even K is handled only by adding a virtual user.
  • standard math The PDA-to-caching-scheme equivalence in Lemma 1 of [9] is accepted as background.
    The entire construction is expressed as a PDA and converted to a caching scheme through this standard mapping.
  • standard math The Lagrange multiplier method gives the claimed optimum for the relaxed real-valued version of Problem 1 (Appendix C).
    The paper relies on standard convex optimization; the induction showing all m_i equal is sketched rather than fully formalized.

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Pith. "Pith review of A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Disjoint Packing." pith.science (2026). https://pith.science/paper/KXYMXNVK

@misc{pith2026250111855,
  author       = {Pith},
  title        = {Pith review of: A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Disjoint Packing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KXYMXNVK}},
  note         = {Machine review of arXiv:2501.11855}
}
abstract

Coded caching is a promising technique to effectively reduce peak traffic by using local caches and the multicast gains generated by these local caches. We prefer to design a coded caching scheme with the subpacketization $F$ and transmission load $R$ as small as possible since these are the key metrics for evaluating the implementation complexity and transmission efficiency of the scheme, respectively. However, most of the existing coded caching schemes have large subpacketizations which grow exponentially with the number of users $K$, and there are a few schemes with linear subpacketizations which have large transmission loads. In this paper, we focus on studying the linear subpacketization, i.e., $K=F$, coded caching scheme with low transmission load. Specifically, we first introduce a new combinatorial structure called non-half-sum disjoint packing (NHSDP) which can be used to generate a coded caching scheme with $K=F$. Then a class of new schemes is obtained by constructing NHSDP. Theoretical and numerical comparisons show that (i) compared to the existing schemes with linear subpacketization (to the number of users), the proposed scheme achieves a lower load; (ii) compared to some existing schemes with polynomial subpacketization, the proposed scheme can also achieve a lower load in some cases; (iii) compared to some existing schemes with exponential subpacketization, the proposed scheme has loads close to those of these schemes in some cases. Moreover, the new concept of NHSDP is closely related to the classical combinatorial structures such as cyclic difference packing (CDP), non-three-term arithmetic progressions (NTAP), and perfect hash family (PHF). These connections indicate that NHSDP is an important combinatorial structure in the field of combinatorial design.

Figures

Figures reproduced from arXiv: 2501.11855 by the authors.

Figure 1
Figure 1. (K, M, N) caching system receiving the request vector d, the sever broadcasts XOR of coded packets with a size of at most RdF to the users such that each user is able to decode its requested file. In this paper, we focus on the normalized amount of transmission for the worst-case over all possible demands which is defined as follows. R = max{Rd | d ∈ [N] K}. (1) The first well-known scheme was proposed in [2], which… view at source ↗
Figure 2
Figure 2. Memory ratio-subpacketization tradeoff for K = 85 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 25 30 35 40 45 50 [PITH_FULL_IMAGE:figures/full_fig_p023_2.png] view at source ↗
Figure 5
Figure 5. Memory ratio-load tradeoff for K = 729 2) Comparison with the polynomial subpacketization schemes in [24], [26]: Since the user numbers of the schemes in [24], [26] are the special integers, including combination numbers, powers, products of combination numbers, and powers, it is difficult for us to directly plot a graph for given values of K. Instead, we compare our scheme with the CKSM scheme and the YTCC scheme b… view at source ↗
Figures from the paper (2 more)
Figure 6
Figure 6. Figure 6: Memory ratio-subpacketization tradeoff for K = 85 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 90 [PITH_FULL_IMAGE:figures/full_fig_p026_6.png]
Figure 8
Figure 8. Figure 8: Memory ratio-subpacketization tradeoff for K = 729 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 700 [PITH_FULL_IMAGE:figures/full_fig_p026_8.png]

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Forward citations

Cited by 2 Pith papers

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  2. On Hierarchical Coded Caching with Offline Users

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Reference graph

Works this paper leans on

48 extracted references · 46 canonical work pages · cited by 2 Pith papers

  1. [29]

    A coded caching scheme with linear sub-packetization and its application to multi- access coded caching,

    A. A. Mahesh and B. Sundar Rajan, “A coded caching scheme with linear sub-packetization and its application to multi- access coded caching,” in Proc. IEEE Inf. Theory Workshop (ITW) , Apr. 2021, pp. 1–5

    work page 2021

  2. [16]

    Coded caching schemes with linear subpacketizations,

    X. Zhong, M. Cheng, and R. Wei, “Coded caching schemes with linear subpacketizations,” IEEE Transactions on Communications, vol. 69, no. 6, pp. 3628–3637, 2021

    work page 2021

  3. [20]

    Lifting constructions of pdas for coded caching with linear subpacketization,

    V . R. Aravind, P. K. Sarvepalli, and A. Thangaraj, “Lifting constructions of pdas for coded caching with linear subpacketization,” IEEE Transactions on Communications , vol. 70, no. 12, pp. 7817–7829, 2022

    work page 2022

  4. [24]

    Placement delivery array design through strong edge coloring of bipartite graphs,

    Q. Yan, X. Tang, Q. Chen, and M. Cheng, “Placement delivery array design through strong edge coloring of bipartite graphs,” IEEE Commun. Lett. , vol. 22, no. 2, pp. 236–239, Feb. 2018. 36

    work page 2018

  5. [26]

    Subexponential and linear subpacketization coded caching via projective geometry,

    H. H. S. Chittoor, P. Krishnan, K. V . S. Sree, and B. Mamillapalli, “Subexponential and linear subpacketization coded caching via projective geometry,” IEEE Trans. Inf. Theory , vol. 67, no. 9, pp. 6193–6222, Sep. 2021

    work page 2021

  6. [27]

    Coded caching based on combinatorial designs,

    S. Agrawal, K. V . Sushena Sree, and P. Krishnan, “Coded caching based on combinatorial designs,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , Jul. 2019, pp. 1227–1231

    work page 2019

  7. [30]

    Multi-access coded caching scheme with linear sub-packetization using pdas,

    S. Sasi and B. S. Rajan, “Multi-access coded caching scheme with linear sub-packetization using pdas,” IEEE Transactions on Communications , vol. 69, no. 12, pp. 7974–7985, 2021

    work page 2021

  8. [1]

    Improving bicm performance of qam constellations for broadcasting applications,

    C. Abdel Nour and C. Douillard, “Improving bicm performance of qam constellations for broadcasting applications,” in Proc. Int. Symp. on Turbo Codes and Related Topics , Sep. 2008, pp. 55–60

    work page 2008

Show all 48 references
  1. [2]

    Fundamental limits of caching,

    M. A. Maddah-Ali and U. Niesen, “Fundamental limits of caching,” IEEE Trans. Inf. Theory, vol. 60, no. 5, pp. 2856–2867, May 2014

    2014

  2. [3]

    On the optimality of uncoded cache placement,

    K. Wan, D. Tuninetti, and P. Piantanida, “On the optimality of uncoded cache placement,” in Proc. IEEE Inf. Theory Workshop (ITW), Sep. 2016, pp. 161–165

    2016

  3. [4]

    Uncoded placement optimization for coded delivery,

    S. Jin, Y . Cui, H. Liu, and G. Caire, “Uncoded placement optimization for coded delivery,” in Proc. 16th Int. Symp. Modeling Optim. Mobile, Ad Hoc, Wireless Netw. (WiOpt) , May 2018, pp. 1–8. 35

    2018

  4. [5]

    The exact rate-memory tradeoff for caching with uncoded prefetching,

    Q. Yu, M. A. Maddah-Ali, and A. S. Avestimehr, “The exact rate-memory tradeoff for caching with uncoded prefetching,” IEEE Trans. Inf. Theory , vol. 64, no. 2, pp. 1281–1296, Feb. 2018

    2018

  5. [6]

    An index coding approach to caching with uncoded cache placement,

    K. Wan, D. Tuninetti, and P. Piantanida, “An index coding approach to caching with uncoded cache placement,” IEEE Trans. Inf. Theory , vol. 66, no. 3, pp. 1318–1332, Mar. 2020

    2020

  6. [7]

    Finite-length analysis of caching-aided coded multicasting,

    K. Shanmugam, M. Ji, A. M. Tulino, J. Llorca, and A. G. Dimakis., “Finite-length analysis of caching-aided coded multicasting,” IEEE Trans. Inf. Theory , vol. 62, no. 10, pp. 5524–5537, Oct. 2016

    2016

  7. [8]

    A generalized grouping scheme in coded caching,

    M. Cheng, J. Jiang, Q. Wang, and Y . Yao, “A generalized grouping scheme in coded caching,” IEEE Trans. Commun. , vol. 67, no. 5, pp. 3422–3430, May 2019

    2019

  8. [9]

    On the placement delivery array design for centralized coded caching scheme,

    Q. Yan, M. Cheng, X. Tang, and Q. Chen, “On the placement delivery array design for centralized coded caching scheme,” IEEE Trans. Inf. Theory , vol. 63, no. 9, pp. 5821–5833, Sep. 2017

    2017

  9. [10]

    Constructions of coded caching schemes with flexible memory size,

    M. Cheng, J. Jiang, Q. Yan, and X. Tang, “Constructions of coded caching schemes with flexible memory size,” IEEE Trans. Commun., vol. 67, no. 6, pp. 4166–4176, Jun. 2019

    2019

  10. [11]

    Some variant of known coded caching schemes with good performance,

    M. Cheng, J. Jiang, X. Tang, and Q. Yan, “Some variant of known coded caching schemes with good performance,” IEEE Trans. Commun., vol. 68, no. 3, pp. 1370–1377, Mar. 2020

    2020

  11. [12]

    A framework of constructing placement delivery arrays for centralized coded caching,

    M. Cheng, J. Wang, X. Zhong, and Q. Wang, “A framework of constructing placement delivery arrays for centralized coded caching,” IEEE Trans. Inf. Theory , vol. 67, no. 11, pp. 7121–7131, Nov. 2021

    2021

  12. [13]

    Placement delivery array construction via cartesian product for coded caching,

    J. Wang, M. Cheng, K. Wan, and G. Caire, “Placement delivery array construction via cartesian product for coded caching,” IEEE Transactions on Information Theory , vol. 69, no. 12, pp. 7602–7626, 2023

    2023

  13. [14]

    Multi-access coded caching with optimal rate and linear subpacketization under pda and consecutive cyclic placement,

    J. Wang, M. Cheng, Y . Wu, and X. Li, “Multi-access coded caching with optimal rate and linear subpacketization under pda and consecutive cyclic placement,” IEEE Transactions on Communications , vol. 71, no. 6, pp. 3178–3190, 2023

    2023

  14. [15]

    Design of coded caching schemes with linear subpacketizations based on injective arc coloring of regular digraphs,

    X. Wu, M. Cheng, L. Chen, C. Li, and Z. Shi, “Design of coded caching schemes with linear subpacketizations based on injective arc coloring of regular digraphs,” IEEE Transactions on Communications , vol. 71, no. 5, pp. 2549–2562, 2023

    2023

  15. [17]

    Placement delivery arrays based on combinatorial designs,

    J. Li and Y . Chang, “Placement delivery arrays based on combinatorial designs,” IEEE Communications Letters , vol. 26, no. 2, pp. 296–300, 2022

    2022

  16. [18]

    Shared cache coded caching schemes with known user-to- cache association profile using placement delivery arrays,

    E. Peter, K. K. Krishnan Namboodiri, and B. Sundar Rajan, “Shared cache coded caching schemes with known user-to- cache association profile using placement delivery arrays,” in 2022 IEEE Information Theory Workshop (ITW) , 2022, pp. 678–683

    2022

  17. [19]

    Design of placement delivery arrays for coded caching with small subpacketizations and flexible memory sizes,

    X. Wu, M. Cheng, C. Li, and L. Chen, “Design of placement delivery arrays for coded caching with small subpacketizations and flexible memory sizes,” IEEE Transactions on Communications , vol. 70, no. 11, pp. 7089–7104, 2022

    2022

  18. [21]

    Coded caching schemes with reduced subpacketization from linear block codes,

    L. Tang and A. Ramamoorthy, “Coded caching schemes with reduced subpacketization from linear block codes,” IEEE Trans. Inf. Theory , vol. 64, no. 4, pp. 3099–3120, Apr. 2018

    2018

  19. [22]

    Centralized coded caching schemes: A hypergraph theoretical approach,

    C. Shangguan, Y . Zhang, and G. Ge, “Centralized coded caching schemes: A hypergraph theoretical approach,” IEEE Trans. Inf. Theory , vol. 64, no. 8, pp. 5755–5766, Aug. 2018

    2018

  20. [23]

    Coded caching with linear subpacketization is possible using ruzsa- szem´eredi graphs,

    K. Shanmugam, A. M. Tulino, and A. G. Dimakis, “Coded caching with linear subpacketization is possible using ruzsa- szem´eredi graphs,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , Jun. 2017, pp. 1237–1241

    2017

  21. [25]

    Multi-access coded caching schemes from cross resolvable designs,

    D. Katyal, P. N. Muralidhar, and B. S. Rajan, “Multi-access coded caching schemes from cross resolvable designs,” IEEE Trans. Commun., vol. 69, no. 5, pp. 2997–3010, May 2021

    2021

  22. [28]

    A rainbow framework for coded caching and its applications,

    M. Xu, Z. Xu, G. Ge, and M.-Q. Liu, “A rainbow framework for coded caching and its applications,” IEEE Transactions on Information Theory , vol. 70, no. 3, pp. 1738–1752, 2024

    2024

  23. [31]

    Some combinatorial constructions for optical orthogonal codes,

    J. Yin, “Some combinatorial constructions for optical orthogonal codes,” Discret. Math. , vol. 185, no. 1-3, pp. 201–219,

  24. [32]

    A density version of a geometric ramsey theorem,

    T. C. Brown and J. P. Buhler, “A density version of a geometric ramsey theorem,” Journal of Combinatorial Theory, Series A, vol. 32, no. 1, pp. 20–34, 1982

    1982

  25. [33]

    Derandomization, witnesses for boolean matrix multiplication and construction of perfect hash functions,

    N. Alon and M. Naor, “Derandomization, witnesses for boolean matrix multiplication and construction of perfect hash functions,” Algorithmica, vol. 16, no. 4, pp. 434–449, 1996

    1996

  26. [34]

    Jukna, Extremal combinatorics: with applications in computer science

    S. Jukna, Extremal combinatorics: with applications in computer science . Springer, 2011, vol. 571

    2011

  27. [35]

    Separating hash families: A johnson-type bound and new constructions,

    C. Shangguan and G. Ge, “Separating hash families: A johnson-type bound and new constructions,” SIAM Journal on Discrete Mathematics, vol. 30, no. 4, pp. 2243–2264, 2016. [Online]. Available: https://doi.org/10.1137/15M103827X

    2016 doi

  28. [36]

    Improving behrend’s construction: Sets without arithmetic progressions in integers and over finite fields,

    C. Elsholtz, Z. Hunter, L. Proske, and L. Sauermann, “Improving behrend’s construction: Sets without arithmetic progressions in integers and over finite fields,” arXiv preprint arXiv:2406.12290 , 2024

    2024 arXiv

  29. [37]

    Perfect hash families of strength three with three rows from varieties on finite projective geometries,

    R. Fuji-Hara, “Perfect hash families of strength three with three rows from varieties on finite projective geometries,” Designs, Codes and Cryptography , vol. 77, no. 2, pp. 351–356, 2015

    2015

  30. [38]

    Placement delivery array based on concatenating construction,

    X. Zhong, M. Cheng, and J. Jiang, “Placement delivery array based on concatenating construction,” IEEE Commun. Lett. , vol. 24, no. 6, pp. 1216–1220, Jun. 2020

    2020

  31. [39]

    Placement delivery arrays from combinations of strong edge colorings,

    J. Michel and Q. Wang, “Placement delivery arrays from combinations of strong edge colorings,” IEEE Trans. Commun. , vol. 68, no. 10, pp. 5953–5964, Oct. 2020

    2020

  32. [40]

    Cryptography theory and practice, chapman &hall/crc,

    D. Stinson, “Cryptography theory and practice, chapman &hall/crc,” 2006

    2006

  33. [41]

    C. J. Colbourn, CRC handbook of combinatorial designs . CRC press, 2010

    2010

  34. [42]

    Combinatorics and threshold cryptography,

    S. R. Blackburn, “Combinatorics and threshold cryptography,” in Combinatorial Designs and their Applications . Routledge, 2023, pp. 49–70

    2023

  35. [43]

    Efficient multiplicative sharing schemes,

    S. R. Blackburn, M. Burmester, Y . Desmedt, and P. R. Wild, “Efficient multiplicative sharing schemes,” in International Conference on the Theory and Applications of Cryptographic Techniques . Springer, 1996, pp. 107–118

    1996

  36. [44]

    Roux-type constructions for covering arrays of strengths three and four,

    C. J. Colbourn, S. S. Martirosyan, T. Van Trung, and R. A. Walker, “Roux-type constructions for covering arrays of strengths three and four,” Designs, Codes and Cryptography , vol. 41, pp. 33–57, 2006

    2006

  37. [45]

    Broadcast encryption,

    A. Fiat and M. Naor, “Broadcast encryption,” in Advances in Cryptology — CRYPTO’ 93 , D. R. Stinson, Ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994, pp. 480–491

    1994

  38. [46]

    Bounds and constructions for 3 3¯-separable codes with length 3,

    M. Cheng, J. Jiang, H. Li, Y . Miao, and X. Tang, “Bounds and constructions for 3 3¯-separable codes with length 3,” Designs, Codes and Cryptography , vol. 81, pp. 317–335, 2016. 37

    2016

  39. [47]

    Separating hash families: A johnson-type bound and new constructions,

    C. Shangguan and G. Ge, “Separating hash families: A johnson-type bound and new constructions,” SIAM Journal on Discrete Mathematics, vol. 30, no. 4, pp. 2243–2264, 2016

    2016

  40. [1998]

    Available: https://doi.org/10.1016/S0012-365X(97)00172-6

    [Online]. Available: https://doi.org/10.1016/S0012-365X(97)00172-6

    doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.