Improved methods for deriving the complete weight distribution of reed‐solomon codes
Kin‐ichiroh Tokiwa, Hatsukazu Tanaka · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract The authors previously considered the problem of deriving the complete weight distribution (CWD) of Reed‐Solomon (RS) codes and developed a formula which established the relationship between a specific codeword set and the CWD of an RS code. If this formula is used, then the CWD of an RS code can be determined by examining fewer codewords than would be required by an exhaustive search. However, subsequent investigation showed that this formula can be applied in its current form only to codes with prime length and not to codes with composite length. A new form of this formula given herein does not depend on whether the code length is prime or composite. the set of codewords that must be examined to determine the CWD of an RS code is respecified and a formula that gives the relationship between this newly specified codeword set and the CWD of an RS code is derived. It is also shown that, when the generator polynomial of an RS code does not have unity as a root, then the number of codewords that must be examined can be reduced even further.