On Niho type cross-correlation functions of m-sequences

On Niho type cross-correlation functions of m-sequences

Assume that d ≡ 1 (mod q − 1). We study the number of solutions to (x + 1)d = xd + 1 in GF(q2). In addition, we give a simple proof of the fact that the cross-correlation function between two m-sequences, which differ by a decimation of this type, is at least four-valued. © 2005 Elsevier Inc. All rights reserved.

Niho Type Cross-Correlation Functions and Related Equations Niho Type Cross-Correlation Functions and Related Equations

$p$-ary sequences with six-valued cross-correlation function: a new decimation of Niho type

For an odd prime p and n = 2m, a new decimation d = (p−1) 2 +1 of Niho type ofm-sequences is presented. Using generalized Niho’s Theorem, we show that the cross-correlation function between a p-ary m-sequence of period pn−1 and its decimated sequence by the above d is at most six-valued and we can easily know that the magnitude of the cross correlation is upper bounded by 4 √ p − 1.

A Note on Cross Correlation Distribution of Ternary m-Sequences

In this note, we prove a conjecture proposed by Tao Zhang, Shuxing Li, Tao Feng and Gennian Ge, IEEE Transaction on Information Theory, vol. 60, no. 5, May 2014. This conjecture is about the cross correlation distribution of ternary m-sequences.

Some New Results on the Cross Correlation of $m$-sequences

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 − 1, we determine the cross correlation distribution for decimations d = 3 + 2 and d = 3 + 2, where gcd(r, 3) = 1. Meanwhile, for a binary m-sequence of period 2 − 1, we make an initial investigation for the decimatio...