Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
AN ALGORITHMIC APPROACH TO ACHIEVE MINIMUM $\\ ho$-DISTANCE AT LEAST d IN LINEAR ARRAY CODES
Sapna JAIN
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2008 Volume 62 Issue 1 Pages 189-200

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Abstract

An array code/linear array code is a subset/subspace, respectively, of the linear space Matm×s(Fq), the space of all m × s matrices with entries froma finite field Fq endowed with a non-Hamming metric known as the RT-metric or $\\ ho$-metric or m-metric. In this paper, we obtain a sufficient lower bound on the number of parity check digits required to achieve minimum $\\ ho$-distance at least d in linear array codes using an algorithmic approach. The bound has been justified by an example. Using this bound, we also obtain a lower bound on the numberBq(m × s, d) where Bq(m × s, d) is the largest number of code matrices possiblein a linear array code V ⊆ Mat m × s (Fq) having minimum $\\ ho$-distance at least d.

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© 2008 by Faculty of Mathematics, Kyushu University
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