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Duality Preserving Gray Maps for Codes over Rings
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
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