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

The purpose of this paper is to determine the p-adic complexity of the Ding-Helleseth-Martinsen (DHM) sequences with period N=2q, where q \equiv 5\pmod 8 is a prime number. We firstly use the p-adic exponential valuation, cyclotomic numbers of order four, "Gauss periods" and "quadratic Gauss sums" on finite field \mathbbF_q and valued in \mathbbZ_p.N-1 to determine the p-adic complexity of the DHM sequences.