The syndromes decoding algorithm in group codes
Consuelo Martı́nez, Fabián Molina · Finite Fields and Their Applications · 2023
Our aim is the design of an efficient decoding algorithm in group codes. The algorithm is inspired by the well known syndrome decoding algorithm for linear codes and uses the decomposition of a semisimple group algebra KG as a direct sum of two-sided ideals, each of them generated by a central idempotent of KG. When G is an abelian group the algorithm can be modified to make it very simple and efficient. Some illustrative examples are presented.