Title of article :
Computation of Minimum Hamming Weight for Linear Codes
Author/Authors :
Rostami, Esmaeil Department of Pure Mathematics - Faculty of Mathematics and Computer - Shahid Bahonar University of Kerman, Kerman, Iran , Nekooei, Reza Department of Pure Mathematics - Faculty of Mathematics and Computer - Shahid Bahonar University of Kerman, Kerman, Iran
Abstract :
In this paper, we consider the minimum Hamming weight
for linear codes over special finite quasi-Frobenius rings. Furthermore,
we obtain minimal free R-submodules of a finite quasi-Frobenius ring R
which contain a linear code and derive the relation between their minimum
Hamming weights. Finally, we suggest an algorithm that computes
this weight using the Grobner basis and we show that under certain conditions
a linear code takes the maximum of minimum Hamming weight.
Keywords :
SPAP-ring , Grobner basis , quasi-Frobenius ring , Linear code , Algebraic coding theory
