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For an odd prime p congruent to 3 modulo 4 and an odd integer n, a new family of p-ary sequences of period N=(pn-1)/2 with low correlation is proposed. The family is constructed by shifts and additions of two decimated m-sequences with the decimation factors 2 and 2d, d = N - pn-1. The upper bound for the maximum magnitude of nontrivial correlations of this family is derived using well known Kloosterman...
In this paper, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel'nikov sequences. The frequency of each autocorrelation value of an M-ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is...
In this paper, we derive the cyclotomic numbers of order 5 over an extension field Fpn using the well-known results of quintic Jacobi sums over Fp (B. C. Berndt, et al., 1998). For p ne 1 mod 5, we have obtained the simple closed-form expression of the cyclotomic numbers of order 5 over Fpn. For p equiv 1 mod 5, we express the cyclotomic number of order 5 over F pn in terms of the solution of the...
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