On minimal easily computable dimension group algebras, and group codes
E. J. Garc\'ia-Claro
TL;DR
This paper characterizes finite semisimple group algebras with easily computable minimal ideals and provides bounds on the minimum Hamming distance of group codes within these algebras.
Contribution
It introduces a characterization of ECD group algebras and establishes lower bounds for the minimum Hamming distance of associated group codes.
Findings
Characterization of ECD semisimple group algebras
Lower bounds for Hamming distance of group codes
Examples illustrating the main results
Abstract
Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples illustrating the main results are provided.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding