Computation of Minimum Hamming Weight for Linear Codes

Author(s):

E. Rostami* , R. Nekooei

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
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:

Algebraic coding theory , Linear codes , Quasi-Frobenius rings , Grobner basis , SPAP-rings

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:14 Issue: 1, May 2019
Pages:
81 to 93
https://www.magiran.com/p1956537