2025/08/08 by Monica Nevins, Nevins, Monica, Susanne Pumpluen +1 · 1 citation
Computer Science · Mathematics · #11T71 #17A99 #81P70 #94B15 #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2508.06695
openalex publication_date 2025/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We work in the setting of linear skew constacyclic codes over a commutative base ring S. We show that the notions of (n,σ)-isometry and (n,σ)-equivalence introduced by Ou-azzou et al coincide for most skew (σ,a)-constacyclic codes of length n. To prove this, we show that all Hamming-weight preserving isomorphisms between their ambient rings which extend some automorphism τ of S that commutes with σ must have degree one, when those rings are not associative. In the process we determine isomorphisms between their nonassociative ambient rings, the Petit rings S[t;σ]/S[t;σ](tn-a), which give rise to skew constacyclic codes. As a consequence, we propose new definitions of equivalence and isometry of skew constacyclic codes that exactly capture all Hamming-weight preserving isomorphisms between the ambient rings of skew constacyclic codes which extend τ∈ \rm Aut(S) that commute with σ, and lead to tighter classifications.