Duality Preserving Gray Maps for Codes over Rings
Information Theory
2016-08-08 v2 math.IT
Rings and Algebras
Abstract
Given a finite ring which is a free left module over a subring of , two types of -bases, pseudo-self-dual bases (similar to trace orthogonal bases) and symmetric bases, are defined which in turn are used to define duality preserving maps from codes over to codes over . Both types of bases are generalizations of similar concepts for fields. Many illustrative examples are given to shed light on the advantages to such mappings as well as their abundance.
Keywords
Cite
@article{arxiv.1505.07493,
title = {Duality Preserving Gray Maps for Codes over Rings},
author = {Steve Szabo and Felix Ulmer},
journal= {arXiv preprint arXiv:1505.07493},
year = {2016}
}