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New Family of pary Sequences with Optimal Correlation Property 1

For an odd prime p and an integer n = (2m + 1)k, a new family of p-ary sequences with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation. Period of the sequences is p − 1 and the size of family is p. It is also derived that the linear span of the sequences in the family is (m+2) ·n except the m-sequence in the family. The maximum nontrivial correlation value Rmax does not exceed 1 + √ pn, which means the optimal correlation property in terms of Welch’s lower bound.