Cyclicity of Binary Group Codes
Abstract
In this paper, we study the cyclicity of binary group codes, identifying them as ideals in a group algebra. We focus on the construction of ω|ω¯ codes, proving that they are self-dual group codes over the abelian group C2×Ck. We demonstrate that for even integers k>2, if the polynomial xk-1 splits into self-reciprocal irreducible factors, these codes are not permutationally equivalent to any cyclic code. Additionally, we present computational results for binary group codes of length n
Fields of Study & Subjects
Coding theory and cryptography
Finite Group Theory Research
Error Correcting Code Techniques
Publication details
- Journal / source
- Entropy
- Volume
- 28
- Issue
- 3
- Pages
- 289–289
- Publication date
- 4 March 2026
- Language
- EN