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In this paper, we show that the generalization by D.S.Kim in 2010 for the construction of sequence family of period q−1 using the Sidelnikov sequences of period qd−1 can be further generalized by removing the condition that gcd(q − 1, d) = 1. It turned out that the correlation bound remains the same and the size of the family is almost the same as the one with the previous condition.
In this paper, we show that the d-decimation of a Sidelnikov sequence is the d-multiple of another Sidelnikov sequence and vice versa. Also, we calculate the crosscorrelation magnitude between d- and d′-decimations of a Sidelnikov sequence of period q − 1 to be upper bounded by (d+d′ − 1) √q+3.
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