Binary Sequences with Optimal Correlations and Large Linear Span

A family of binary sequences is presented and proved to have optimal correlations and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. A lower bound on the linear span of the family is provided. With suitable choices of parameters, it is proved that the family has exponentially larger linear spans than both No sequences and TN sequences.

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