On the Complete Weight Enumerators of Doubly-Extended Reed-Solomon Codes
Toshiyuki Kohnosu · 2004
The complete weight enumerator (cwe) of a code classifies the set of codewords according to the number of times that each field element appears in each codeword. The cwe gives more information on structure of a code, so it is useful to obtain the cwe. The cwe’s of ReedSolomon (RS) codes of small dimensions and their extended codes have been shown in [1][2]. It has been discussed the problem of deriving the cwe of RS codes in [3][4]. In this paper, we derive the cwe’s of doublyextended RS codes of dimensions two and three. As an application of the cwe’s, we show the ordinary Hamming weight enumerator of the binary code obtained from the doubly-extended RS code by replacing each field element with its binary representation.