A New Sequence Families With Low Correlation Derived From Multiplicative And Additive Characters

Power residue and Sidelnikov sequences are polyphase sequences with low correlation represented by multiplicative characters. In this paper, sequence families constructed from the shift and addition of the polyphase sequences are discussed by new approach.Firstly, utilizing the new Weil bound theorem, the maximum magnitude of correlation are calculated and compared with previous results. The new Weil bound theorem on multiplicative character sums is redefined for the χ(0) = 1, where the character sums are equivalent to the correlations of sequences represented by multiplicative characters.Then based on the known result of [2], using the same approach, two new constructions with large family sizes and low maximum correlation are given. For positive integers d √p and M | p- 1, The first new construction is the sequence family ?(c1,c2)d,pwith period p consists of((M- 1)2·p-12)pdsequences. For positive integers d √q and M |pm- 1, Another new construction is the sequence family Γ(c1,c2)d,qwith period pm- 1 consists of((M-1)2(q-1)-M(M-1)2) · qd- dp sequences. Then utilizing the new Weil bound theorem and additive multiplicative character sums, we prove that the corresponding maximum magnitude of correlation is(d + 3)√p + 4 and(d + 3)√q + 5 respectively. Finally, the low correlation properties in this paper and the sequence families previously constructed are compared.