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.
Skew polycyclic over finite chain rings associated to trinomials
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This work studies skew polycyclic codes over finite chain rings defined by central trinomials. For this class of codes, we investigate Hamming equivalence in the non-commutative (skew) setting. We introduce an equivalence relation on the defining trinomials and demonstrate that it admits a group-theoretic characterization in terms of a group of binomials equipped with the Schur multiplication. We determine the conditions under which skew polycyclic codes are Hamming equivalent to those defined by the specific trinomial $x^n-(x^\ell+1)$. This reduces the classification problem for these codes, up to Hamming equivalence, to a canonical case. Finally, we determine the size of the corresponding equivalence class using the decomposition of the unit group of the underlying chain ring.
fields
cs.IT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Skew Constacyclic Codes Of Length $np^s$ over $ \frac{\mathbb{F}_{p^m}[u]}{\langle u^k \rangle}
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.