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

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 Helleseth-Gong sequences. Period of the sequences is pⁿ-1 and the size of family is pⁿ. 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 R_max does not exceed 1+√(Pⁿ) which means the optimal correlation property in terms of Welch´s lower bound.