The binary weight distribution of the extended (2 m,2 m-4) code of the Reed-Solomon code over GF(2 m) with generator polynomial (x-\(\alpha\) )(x- \(\alpha\) 2)(x-\(\alpha\) 3) (Q1106181)

Let C be an [n,k] linear code over GF(2 m). The binary [nm,km] linear code obtained from C by representing each code symbol by the corresponding binary m-tuple using given basis of GF(2 m) over GF(2), is called binary image of C. Some general results such as the description of the dual code of a binary image of a code and a lower bound on the minimum weight of a binary image of a cyclic code are presented in the paper. Also, the weight enumerator for a binary image of the extended (2 m,2 m-4) Reed-Solomon code over GF(2 m) with generator polynomial (x- \(\alpha)\)(x-\(\alpha\) 2)(x-\(\alpha\) 3) where \(\alpha\) is a primitive element of GF(2 m).