AN ALGORITHMIC APPROACH TO ACHIEVE MINIMUM $\\rho$-DISTANCE AT LEAST d IN LINEAR ARRAY CODES
Sapna Jain · Kyushu Journal of Mathematics · 2008
An array code/linear array code is a subset/subspace, respectively, of the linear space Mat m×s (F q ), the space of all m × s matrices with entries from a finite field F q endowed with a non-Hamming metric known as the RT-metric or ρ-metric or m-metric.In this paper, we obtain a sufficient lower bound on the number of parity check digits required to achieve minimum ρ-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 number B q (m × s, d) where B q (m × s, d) is the largest number of code matrices possible in a linear array code V ⊆ Mat m×s (F q ) having minimum ρ-distance at least d.