Duality preserving Gray maps for codes over rings
Steve Szabo, Félix Ulmer · Journal of Algebra and Its Applications · 2016
Given a finite ring [Formula: see text] which is a free left module over a subring [Formula: see text] of [Formula: see text], two types of [Formula: see text]-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 [Formula: see text] to codes over [Formula: see text]. 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.