TITLE:
Images of Linear Block Codes over Fq+uFq+vFq+uvFq
AUTHORS:
Jane D. Palacio, Virgilio P. Sison
KEYWORDS:
q-ary Images; Distance Bounds
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.3 No.1B1,
July
11,
2013
ABSTRACT: In this paper, we considered linear block codes over Rq=Fq+uFq+vFq+uvFq, u2=v2=0,uv=vu where q=pm, m∈N . First we looked at the structure of the ring. It was shown
that Rq 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 Rq over Fq . Bounds on the minimum Hamming distance of the image codes
were then derived. A code meeting such bounds is given as an example.