On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences
On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences
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DOI：
10.1109/tit.2020.2964171
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发表时间：
2019-04
影响因子：
2.5
通讯作者：
Lulu Zhang;Jun Zhang;Minghui Yang;K. Feng
中科院分区：
文献类型：
--
作者：
Lulu Zhang;Jun Zhang;Minghui Yang;K. Feng
利用有限域$\mathbb {F}_{{q}}$上的四阶分圆数、“高斯周期”和“二次高斯和”，确定了值为$\mathbb {Z}_{2^{{N}}-1}$的Ding-Helleseth-Martinsen（DHM）二元序列的2-adic复杂度，其中${q} \equiv 5\pmod 8$是素数，${N}=2{q}$是DHM序列的周期。
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 sums” 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 ${N}=2{q}$ is the period of the DHM sequences.