577 research outputs found
On the Weight Distribution of Codes over Finite Rings
Let R > S be finite Frobenius rings for which there exists a trace map T from
R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is
an S-linear subring-subcode of a left linear code over R. We consider functions
f for which the homogeneous weight distribution of C can be computed. In
particular, we give constructions of codes over integer modular rings and
commutative local Frobenius that have small spectra.Comment: 18 p
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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