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

Abstract

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 $q\equiv 5(\mathrm{mod}8)$ is a prime number and $N=2q$ is the period of the DHM sequences.

16 pages