An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function

In this paper, let n = 2k and d = 3 · 2^k - 2 with k ≥ 3 and gcd(d, 2ⁿ - 1) = 1. Based on some analysis of certain equations over finite fields and the number of codewords with Hamming weight five in Zetterberg code, the correlation distribution between a binary m-sequence of period 2ⁿ - 1 and its d-decimation sequence is completely determined. This solves a ten-year-old open problem proposed by Dobbertin et al.