Construction of minimal non-abelian left group codes
Gabriela Olteanu, Inneke Van Gelder
TL;DR
This paper presents algorithms for constructing minimal non-abelian left group codes using primitive idempotents in semisimple group algebras, with applications to improving linear codes over F_2 and F_3.
Contribution
It introduces new algorithms for minimal non-abelian left group codes based on primitive idempotents in group algebra components.
Findings
Constructed alternative codes to some best linear codes over F_2 and F_3.
Provided a complete set of orthogonal primitive idempotents for certain group algebras.
Demonstrated the effectiveness of the algorithms through examples.
Abstract
Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra FG for a large class of groups G. As an illustration of our methods, alternative constructions to some best linear codes over F_2 and F_3 are given.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · graph theory and CDMA systems