A New Family of p-Ary Sequences of Period (p(n)-1)/2 With Low Correlation

Abstract

For an odd prime p congruent to 3 modulo 4 and an odd integer n, a new family of p-ary sequences of period N = p(n)-1/2 with low correlation is proposed. The family is constructed by shifts and additions of two decimated m-sequences with the decimation factors 2 and 2d, d = N - p(n-1). The upper bound for the maximum magnitude of nontrivial correlations of this family is derived using well known Kloosterman sums. The upper bound is shown to be 2 root N + 1/2 = root 2p(n), which is twice the Welch's lower bound and approximately 1.5 times the Sidelnikov's lower bound. The size of the family is 2(p(n) - 1), which is four times the period of sequences.