On the Weight Distribution of Codes over Finite Rings
Rings and Algebras
2011-01-10 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.1101.1505,
title = {On the Weight Distribution of Codes over Finite Rings},
author = {Eimear Byrne},
journal= {arXiv preprint arXiv:1101.1505},
year = {2011}
}
Comments
18 pg