On Niho type cross-correlation functions of m-sequences

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.

On the Correlation Distribution for a Ternary Niho Decimation

In this paper, let n = 2m and d = 3 − 2 with m ≥ 2 and gcd(d, 3n − 1) = 1. By studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over the finite field F3n , the correlation distribution between a ternarym-sequence of period 3n−1 and its d-decimation sequence is completely determined. This is the first time that the correlation...

On Welch-Gong Transformation Sequence Generators

Welch-Gong (WG) transformation sequences are binary sequences of period 2 − 1 with 2-level auto correlation. These sequences were discovered by Golomb, Gong and Gaal in 1998 and verified for 5 ≤ n ≤ 20. Later on, No, Chung and Yun found another way to construct the WG sequences and verified their result for 5 ≤ n ≤ 23. Dillon first proved this result for odd n in 1998, and finally, Dobbertin an...

Cross-Correlations of Quadratic Form Sequences in Odd Characteristic

Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in odd characteristic. These sequences are shown to have low cross-correlation values in certain cases. They also have significantly higher linear spans than previously studied geometric sequences. These results show that geometric sequences are candidates for use in spread-spectrum communic...