On the 2-Adic Complexity of the Ding-Helleseth-Martinsen Binary Sequences
Lulu Zhang, Jun Zhang, Minghui Yang, Keqin Feng
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 sums” on finite field Fq and valued in Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2N-1</sub> , where q ≡ 5 (mod 8) is a prime number and N = 2q is the period of the DHM sequences.
Topics & Concepts
GaussFinite fieldQuadratic Gauss sumGauss sumBinary numberPrime (order theory)MathematicsQuadratic residueQuadratic equationPrime numberCombinatoricsOrder (exchange)Discrete mathematicsBinary quadratic formField (mathematics)Quadratic fieldArithmeticPure mathematicsPhysicsQuadratic functionQuantum mechanicsGeometryEconomicsFinanceCoding theory and cryptographygraph theory and CDMA systemsCellular Automata and Applications