A fast algorithm for the decoding of binary BCH codes

It is shown how to determine the error locator polynomial of a primitive, binary t-error correcting BCH code directly. Towards this end the set of t syndrome polynomial equations is transformed into an equivalent set of equations, by making use of the Buchberger (1985) algorithm for polynomial reduction. This results in the so-called reduced Grobner basis for a set of polynomial equations, and allows the direct solution of the error locator polynomial. For small number of errors this leads to a substantial reduction in decoding complexity