Adding two information symbols to certain nonbinary BCH codes and some applications

This paper is a compendium of results based on a simple observation: two information symbols can be appended to certain nonbinary BCH codes without affecting the guaranteed minimum distance of these codes. We give two formulations which achieve this result; the second yields information regarding the weights of coset leaders for the original BCH codes. Single-error-correcting Reed-Solomon codes with the added information symbols yield perfect codes for the Hamming metric. We use these lengthened Reed-Solomon codes as building blocks for perfect single-error-correcting codes in another metric.