Decoding the triple-error-correcting (15, 5) binary BCH code by the analytic solution of the cubic error-locator polynomial over GF(24)

Abstract

This paper describes a decoding algorithm for the triple-error-correcting (15, 5) binary BCH code based on the analytic solution of the cubic error-locator polynomial over the extension field GF(24). It is shown that the error-location numbers can be determined directly from the coefficients of the error-locator polynomial. The algorithm avoids the need for a Chien-type search and requires significantly fewer mathematical operations over GF(24) than a Chien-type search.