MDS Array Codes with Independent Parity Symbols

Abstract

A new family of maximum distance separable (MDS) array codes is presented. The code arrays contain p information columns and r independent parity columns, where p is a prime. We give necessary and sufficient conditions for our codes to be MDS, and then prove that if p belongs to a certain class of primes these conditions are satisfied up to r⩽8. We also develop efficient decoding procedures for the case of two and three column errors, and any number of column erasures. Finally, we present upper and lower bounds on the average number of parity bits which have to be updated in an MDS code over GF(2^m), following an update in a single information bit. We show that the upper bound obtained from our codes is close to the lower bound and does not depend on the size of the code symbols.