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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 ≡ 5 (mod 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 Fq and valued in ZpN?1 to determine the p-adic complexity of the DHM sequences.