An algorithmic approach to achieve minimum ρ-distance at least d in linear array codes

Abstract

An array code/linear array code is a subset/subspace, respectively, of the linear space Matmxs (Fq), the space of all x s matrices with entries from a finite field Fq 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 Bq (m x s, d) where Bq (m x s, d) is the largest number of code matrices possible in a linear array code V ⊆ Matm x s, (Fq) having minimum ρ-distance at least d.