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A family of binary sequences is presented and proved to have optimalcorrelation property and large linear span. It includes the small set of Kasamisequences, No sequence set and TN sequence set as special cases. An explicitlower bound expression on the linear span of sequences in the family is given.With suitable choices of parameters, it is proved that the family hasexponentially larger linear spans than both No sequences and TN sequences. Aclass of ideal autocorrelation sequences is also constructed and proved to havelarge linear span.Comment: 21 page

ieice transactions on fundamentals of electronics, communications and computer sciences/ieice transactions on fundamentals of electronics, communications and computer science

A Family of Binary Sequences with 4-Valued Optimal Out-of-Phase Correlation and Large Linear Span