AN ALGORITHMIC APPROACH TO ACHIEVE MINIMUM $\\rho$-DISTANCE AT LEAST d IN LINEAR ARRAY CODES

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.