Construction of minimal non-abelian left group codes

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 $\F G$ 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.

Publication year:2015

Keywords:group codes, linear codes, primitive idempotents, Wedderburn decomposition, finite group algebras

CSS-citation score:1