OJAppS  Vol.3 No.1 B1 , April 2013
Images of Linear Block Codes over Fq+uFq+vFq+uvFq
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.

Cite this paper
J. Palacio and V. Sison, "Images of Linear Block Codes over Fq+uFq+vFq+uvFq," Open Journal of Applied Sciences, Vol. 3 No. 1, 2013, pp. 27-31. doi: 10.4236/ojapps.2013.31B1006.
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