New family of p-ary sequences with optimal correlation property and large linear span

Abstract

For an odd prime p and integer n, m and k such that n=(2m＋1)ㆍk, a new family of p-ary sequences of period p -1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p . That is, the maximum nontrivial correlation value R of all pairs of distinct sequences in the family does not exceed p 2/ ＋1, which means the optimal correlation property in terms of Welch's lower bound. It is also derived that the linear span of the sequences in the family is (m＋2)ㆍn except for the m-sequence in the family.