Unusual general error locator polynomial for the (23, 12, 7) golay code

Abstract

For algebraic decoding of the (23, 12, 7) Golay code, this letter proposes a new error locator polynomial, called the unusual general error locator polynomial, whose coefficients are expressed as a sum of powers of their previous ones. Because of this special property, the determination of such a polynomial can be terminated earlier, and the number of errors occurred can be recognized at the same time.