2009/01/13 by Carl Bracken, Tor Helleseth, Bracken, Carl +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0901.1827
7 pages, submitted to ISIT 2009
arxiv created 2009/01/13 · openalex publication_date 2009/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The binary primitive triple-error-correcting BCH code is a cyclic code of minimum distance 7 with generator polynomial having zeros α, α3 and α5 where α is a primitive root of unity. The zero set of the code is said to be 1,3,5. In the 1970's Kasami showed that one can construct similar triple-error-correcting codes using zero sets consisting of different triples than the BCH codes. Furthermore, in 2000 Chang et. al. found new triples leading to triple-error-correcting codes. In this paper a new such triple is presented. In addition a new method is presented that may be of interest in finding further such triples.