Some New Results on the Cross Correlation of m-sequences

2013/09/30 by Zhang, Tao, Li, Shuxing, Feng, Tao +1
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1309.7734

Abstract

The determination of the cross correlation between an m-sequence and its decimated sequence has been a long-standing research problem. Considering a ternary m-sequence of period 3^3r-1, we determine the cross correlation distribution for decimations d=3^r+2 and d=3^2r+2, where gcd(r,3)=1. Meanwhile, for a binary m-sequence of period 2^2lm-1, we make an initial investigation for the decimation d=\frac2^2lm-12^m+1+2^s, where l ≥ 2 is even and 0 ≤ s ≤ 2m-1. It is shown that the cross correlation takes at least four values. Furthermore, we confirm the validity of two famous conjectures due to Sarwate et al. and Helleseth in this case.

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