2025/07/07 by José Gómez-Torrecillas, Gómez-Torrecillas, José, José Patricio Sánchez-Hernández +1
Computer Science · Engineering · #16S36 #16U20 #16W60 #94B10 #Coding theory and cryptography #FOS: Mathematics #Rings and Algebras (math.RA) #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2507.05022
openalex publication_date 2025/07/07 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
Convolutional codes were originally conceived as vector subspaces of a finite-dimensional vector space over a field of Laurent series having a polynomial basis. Piret and Roos modeled cyclic structures on them by adding a module structure over a finite-dimensional algebra skewed by an algebra automorphism. These cyclic convolutional codes turn out to be equivalent to some right ideals of a skew polynomial ring built from the automorphism. When a skew derivation is considered, serious difficulties arise in defining such a skewed module structure on Laurent series. We discuss some solutions to this problem which involve a purely algebraic treatment of the left skew Laurent series built from a left skew derivation of a general coefficient ring, when possible.