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

For an odd prime p and integers n, m, and k such that n=(2m+1)k, a new family of p-ary sequences of period pⁿ-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 pⁿ. That is, the maximum nontrivial correlation value R_max of all pairs of distinct sequences in the family does not exceed pⁿ2/+1, which means the family has optimal correlation in terms of Welch´s lower bound. The symbol distribution of the sequences in the family is enumerated. It is also shown that the linear span of the sequences in the family is (m+2)n except for the m-sequence in the family.