The Weight Distribution of C5(1, n)

Abstract

In [2] the codes Cq(r, n) over double-struck F signq were introduced. These linear codes have parameters [2n, ∑i=0 r (i n), 2n-r], can be viewed as analogues of the binary Reed-Muller codes and share several features in common with them. In [2], the weight distribution of C3(1, n) is completely determined. In this paper we compute the weight distribution of C5(1, n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials and Lucas numbers. We prove an effective result on the set of Lucas numbers which are powers of two to arrive to the complete determination of the weight distribution of C5(1, n). The final result is stated as Theorem 2.