Skew Constacyclic and LCD Codes over $ \mathbb{F}_{q}+v \mathbb{F}_{q} $
Ranya D.Boulanouar, Aicha Batoul
TL;DR
This paper investigates the properties and equivalences of skew constacyclic, cyclic, and negacyclic codes over semi-local rings, providing constructions, enumeration, and optimal examples of LCD codes with applications to Gray images.
Contribution
It establishes conditions for code equivalency over semi-local rings and introduces new constructions and enumerations of Euclidean and Hermitian skew LCD codes over specific ring extensions.
Findings
Conditions for code equivalency over semi-local rings
Construction and enumeration of Euclidean and Hermitian skew LCD codes
Identification of several optimal LCD codes from Gray images
Abstract
The aim of this paper is to give conditions for the equivalency between skew constacyclic codes, skew cyclic codes and skew negacyclic codes defined over semi-local rings. Also, we provide construction and an enumeration of Euclidean and Hermitian skew LCD cyclic codes over . Several optimal LCD codes are obtained from Gray images of LCD skew codes over semi-local rings.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · graph theory and CDMA systems