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

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=(pⁿ-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√(N+1/2) = √(2pⁿ) , 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(pⁿ-1) , which is four times the period of sequences.