b-Adjacent Error Correction

Abstract

A high-speed method is derived for single-symbol error correcting Reed-Solomon and Hamming type codes. A matrix description is used for implementation of the codes, in which single-error correction in the Galois field 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> corresponds to correcting a block of b bits in a binary field. The resulting codes correct not only single-bit errors but also single clusters of b-adjacent-bit errors.