Technical Report CS-2005-09

Title: Lowest-density MDS codes over extension alphabets
Authors: Erez Louidor, Ron M. Roth
Abstract: Let F be a finite field and b be a positive integer. A construction is presented of codes over the alphabet F^b with the following three properties: (i) the codes are MDS over F^b, (ii) they are linear over F, and (iii) they have systematic generator and parity-check matrices over F with the smallest possible number of nonzero entries. Furthermore, for the case F = GF(2), the construction is the longest possible among all codes that satisfy properties (i)-(iii).
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