Unusual General Error Locator Polynomials for Single-Syndrome Decodable Cyclic Codes

A cyclic code is called single-syndrome decodable if its decoding up to error-correcting capability is completely based on the single syndrome. This letter proposes a construction method of the unusual general error locator polynomial (GELP) for the triple- and quadruple-error-correcting single-syndrome decodable cyclic (SSDC) codes and gives an upper bound on the computational complexity of the unusual GELP. Both theoretical and experimental results show that the unusual GELP has lower computational complexity than the conventional GELP for triple-error-correcting SSDC codes.