Images of Linear Block Codes over Fq+uFq+vFq+uvFq

Jane D. Palacio, Virgilio P. Sison

Institute of Mathematical Sciences and Physics, University of the Philippines Los Ba?os, College, Laguna, Philippines.

DOI: 10.4236/ojapps.2013.31B1006                

Abstract

In this paper, we considered linear block codes over R_q=F_q+uF_q+vF_q+uvF_q, u²=v²=0,uv=vu where q=p^m, m∈N . First we looked at the structure of the ring. It was shown that R_q is neither a finite chain ring nor a principal ideal ring but is a local ring. We then established a generator matrix for the linear block codes and equipped it with a homogeneous weight function. Field codes were then constructed as images of these codes by using a basis of R_q over F_q . Bounds on the minimum Hamming distance of the image codes were then derived. A code meeting such bounds is given as an example.

Keywords

q-ary Images; Distance Bounds

Conflicts of Interest

The authors declare no conflicts of interest.

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