Fast efficient decoder for low distance rs and bch codes

Abstract

An illustrative decoder includes: a syndrome calculator, a location finder, and an error corrector. The syndrome calculator has an array of logic gates to obtain syndrome values as a product of a receive message vector and a parity check matrix, the syndrome values including at least a three ten-bit syndrome values S, S, and S. The location finder derives a number of errors from the syndrome values, and uses a second array of logic gates to obtain two polynomial roots as a product of a syndrome value vector and a quadratic solution matrix when the number of errors is two, the quadratic solution matrix corresponding to a determination of a quadratic equation's trailing coefficient value s, a determination of the quadratic equation's roots, and a reversal of a variable substitution. The location finder further determines a bit index for each of the polynomial roots.