An Open Problem on the Distribution of a Niho-Type Cross-Correlation Function
Yongbo Xia, Nian Li, Xiangyong Zeng, Tor Helleseth · IEEE Transactions on Information Theory · 2016
In this paper, let n = 2k and d = 3 · 2k- 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.