Pith Number

pith:7ELPX5GP

pith:2026:7ELPX5GPWMQK5BS7LZG3BBTIOJ

not attested not anchored not stored refs resolved

Skew Constacyclic Codes Of Length $np^s$ over $ \frac{\mathbb{F}_{p^m}[u]}{\langle u^k \rangle}

Manju Khan, Seema Antil, Seema Chahal, Sugandha Maheshwary

Skew constacyclic codes of length np^s over the ring R_k reduce to skew polycyclic codes of length jl associated with a central irreducible divisor f(x)^j of x^{np^s} - λ.

arxiv:2605.15925 v1 · 2026-05-15 · cs.IT · math.IT · math.RA

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\pithnumber{7ELPX5GPWMQK5BS7LZG3BBTIOJ}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Skew constacyclic codes of length np^s over R_k reduce to the study of skew polycyclic codes of length jl associated with a central irreducible divisor f(x)^j of x^{np^s} - λ, and for λ in the base field the left ideals can be classified completely under suitable conditions on Θ.

C2weakest assumption

The existence and centrality of an irreducible divisor f(x) of degree l and multiplicity j in the skew polynomial ring R_k[x; Θ] such that the quotient ring structure directly yields the ideal lattice of the codes (abstract, paragraph on reduction to polycyclic codes).

C3one line summary

The paper classifies left ideals in skew polynomial rings to describe skew constacyclic codes of length np^s over R_k and provides explicit analyses for lengths 3p^s and 6p^s with examples of optimal parameters.

References

41 extracted · 41 resolved · 1 Pith anchors

[1] Finite rings with identity , author=

[2] Elementary Number Theory , author =

[3] Chahal, S. and Maheshwary, S. , TITLE =. Finite Fields Appl. , FJOURNAL =. 2025 , PAGES = 2025

[4] Hesari, R.M. and Samei, K. , TITLE =. Finite Fields Appl. , FJOURNAL =. 2023 , PAGES = 2023

[5] Dinh, H.Q. , TITLE =. J. Algebra , FJOURNAL =. 2010 , NUMBER = 2010

Receipt and verification

First computed	2026-05-20T00:01:45.360873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f916fbf4cfb320ae865f5e4db08668725dd43e6edc51cd286ac4259aef675ba0

Aliases

arxiv: 2605.15925 · arxiv_version: 2605.15925v1 · doi: 10.48550/arxiv.2605.15925 · pith_short_12: 7ELPX5GPWMQK · pith_short_16: 7ELPX5GPWMQK5BS7 · pith_short_8: 7ELPX5GP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7ELPX5GPWMQK5BS7LZG3BBTIOJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f916fbf4cfb320ae865f5e4db08668725dd43e6edc51cd286ac4259aef675ba0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a0aebaec9f2be7a665c26ef19afd99c517da854e3e3f13d17ec6fc53e93064a",
    "cross_cats_sorted": [
      "math.IT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-15T13:07:37Z",
    "title_canon_sha256": "867c7ee4076e616be2aacf08f7c74d5077028f0a9bb97dc5336c8d2692dffc8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15925",
    "kind": "arxiv",
    "version": 1
  }
}