Wenfeng Jiang

Period-different m-sequences with at most four-valued cross correlation

This paper follows the recent work of Helleseth, Kholosha, Johansen, and Ness to study the cross correlation between an m -sequence of period 2m - 1 and the d-decimation of an m-sequence of a shorter period 2n - 1 for an even number m = 2n. Assuming that d satisfies d(2l + 1) = 2i (mod 2n - 1) for some l > 0 and i > 0, it is proved that the cross correlation takes on either exactly three or four values depending on whether I and n are coprime or not. The distribution of the cross-correlation values is also completely determined. Our results theoretically confirm the numerical data by Ness and Helleseth. It is conjectured that there are no other decimations that give at most four-valued cross correlation apart from the ones proved here.

New Optimal Quadriphase Sequences With Larger Linear Span

In this paper, we construct two new families S and U of optimal quadriphase sequences. Compared to the family A constructed by Boztas et al and family D investigated by Tang et al respectively, the proposed families have the same optimal correlation properties and family size, but larger linear spans.

Two New Families of Optimal Binary Sequences Obtained From Quaternary Sequences

In this paper, we present two optimal binary families of sequences of length 2ⁿ-1 and 2(2ⁿ-1) for odd integer n. They are obtained as the images of proposed optimal quaternary sequences under the most significant bit and the Gray maps. The first family has 2ⁿ+1 sequences of length 2ⁿ-1 and the identical correlation distribution to that of Gold sequences and Gold-like sequences, and the second family of sequences of length 2(2ⁿ-1) has 2ⁿ sequences and the same correlation values as those of Kerdock sequences.

A new family of gold-like sequences

In this paper, for a positive odd integer n, a new family of binary sequences with 2n+1 sequences of length 2n-1 taking three level nontrivial correlations -1 and -1±2(n+1)/2 is presented, whose correlation distribution is the same as that of the well-known Gold sequences. This family may be considered as a new class of Gold-like sequences.

New Family of Binary Sequences with Low Correlation

In this paper, a new family of binary sequences of period 2n-1 with low correlation is proposed for integer n = em and even m. The new family has family size 2n + 1 and maximum nontrivial correlation 2n+e/2 + 1 and 2n+e-1/2 + 1 for even and odd e respectively. Especially, for n = 2m and 3m, we obtain a new family of binary sequences with maximum nontrivial correlation 2n/2 + 1 + 1, and the obtained family is one of the binary families with best correlation among the known families with family size no less than their period 2n-1 for even n. Moreover, the correlation distribution of the new family is also determined.

New Optimal Quadriphase Sequences with Larger Lnear Span

In this paper, we construct two new families S and U of optimal quadriphase sequences. Compared to the family A constructed by Boztas et al and family D investigated by Tang et al respectively, the proposed families have the same optimal correlation properties and family size, but larger linear spans.