New Optimal Binary Sequences with Period $4p$ via Interleaving Ding-Helleseth-Lam Sequences

Linear Complexity of Ding-Helleseth Generalized Cyclotomic Binary Sequences of Any Order

This paper gives the linear complexity of binary Ding-Helleseth generalized cyclotomic sequences of any order.

On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences

We determine the 2-adic complexity of the Ding-Helleseth-Martinsen (DHM) binary sequences by using cyclotomic numbers of order four, "Gauss periods" and "quadratic Gauss sum" on finite field $\mathbb{F}_q$ and valued in $\mathbb{Z}_{2^N-1}$ where $q \equiv 5\pmod 8$ is a prime number and $N=2q$ is the period of the DHM sequences.

A lower bound on the 2-adic complexity of Ding-Helleseth generalized cyclotomic sequences of period $p^n$

Let $p$ be an odd prime, $n$ a positive integer and $g$ a primitive root of $p^n$. Suppose $D_i^{(p^n)}=\{g^{2s+i}|s=0,1,2,\cdots,\frac{(p-1)p^{n-1}}{2}\}$, $i=0,1$, is the generalized cyclotomic classes with $Z_{p^n}^{\ast}=D_0\cup D_1$. In this paper, we prove that Gauss periods based on $D_0$ and $D_1$ are both equal to 0 for $n\geq2$. As an application, we determine a lower bound on the 2-adic complexity of a class of Ding-Helleseth generalized cyclotomic sequences of period $p^n$. The result shows that the 2-adic complexity is at least $p^n-p^{n-1}-1$, which is larger than $\frac{N+1}{2}$…

关于Ding和Helleseth关于最优三元循环码的第9个公开问题

On the Ding and Helleseth's 9th open problem about optimal ternary cyclic codes

本文聚焦Ding等人关于最优三元循环码的第9个公开问题，通过确定有限域上特殊多项式的根集给出不完全解答，并基于此构造了两类满足球填充界的最优三元循环码。

About the Linear Complexity of Ding-Hellesth Generalized Cyclotomic Binary Sequences of Any Period

We defined sufficient conditions for designing Ding-Helleseth sequences with arbitrary period and high linear complexity for generalized cyclotomies. Also we discuss the method of computing the linear complexity of Ding-Helleseth sequences in the general case.

关于 Ding 和 Helleseth 提出的最优三元循环码第8个开放问题

On the Ding and Helleseth's 8th open problem about optimal ternary cyclic codes

针对 Ding 和 Helleseth 的第8个开放问题，本文利用有限域上特殊多项式的根集给出反例与最优性充分条件，并构造一类满足球填充界且不等价于已知码的最优三元循环码。