Deriving the complete weight distribution of reed‐solomon codes
Kin‐ichiroh Tokiwa, Hatsukazu Tanaka · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1993
Abstract The weight distribution of a code usually is investigated on the basis of Hamming weight. For such non‐binary codes as Reed‐Solomon (RS) codes, therefore, all nonzero components of codewords are regarded as identical. To describe the structure of nonbinary codes in more detail, each nonzero component should be distinguished from the other. This requirement can be met by the complete weight distribution (CWD). Recently, Blake and Kith and the present authors derived independently the CWD for a special class of RS codes. However, the derivation of the CWD for general RS codes remains a difficult problem. This paper discusses the problem of obtaining the CWD for general RS codes. To make this process easier, three unique sets of codewords which should be examined are defined first. Then it is shown that the CWD can be derived from such unique sets of codewords. Finally, a relationship between the CWD for RS code of dimension k and that of dimension k + 1 is considered.