Group homomorphisms as error correcting codes

Alan Guo¹

¹Massachusetts Institute of Technology

The electronic journal of combinatorics, Tome 22 (2015) no. 1

Résumé

We investigate the minimum distance of the error correcting code formed by the homomorphisms between two finite groups $G$ and $H$. We prove some general structural results on how the distance behaves with respect to natural group operations, such as passing to subgroups and quotients, and taking products. Our main result is a general formula for the distance when $G$ is solvable or $H$ is nilpotent, in terms of the normal subgroup structure of $G$ as well as the prime divisors of $|G|$ and $|H|$. In particular, we show that in the above case, the distance is independent of the subgroup structure of $H$. We complement this by showing that, in general, the distance depends on the subgroup structure of $H$.

Détail

DOI : 10.37236/4322

Classification : 94B25, 20F99
Mots-clés : group homomorphisms, error correcting codes, minimum distance, solvable groups