A New Family of $p$-Ary Sequences of Period $(p^n-1)/2$ With Low Correlation
Ji-Youp Kim, Sung-Tai Choi, Jong‐Seon No, Habong Chung · IEEE Transactions on Information Theory · 2011
For an odd primepcongruent to 3 modulo 4 and an odd integern, a new family ofp-ary sequences of periodN=(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-pn-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.