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For a prime p and positive integers M and n such that M|p/sup n/-1, Sidel'nikov introduced M-ary sequences (called Sidel'nikov sequences) of period p/sup n/-1, the out-of-phase autocorrelation magnitude of which is upper bounded by 4. In this correspondence, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each… (More)
In this paper, we derive linear complexity over F<sub>p</sub> of the M-ary Sidel'nikov sequences using discrete Fourier transform. As an example, we represent the linear complexity of the ternary Sidel'nikov sequences. It turned out that the ternary Sidel'nikov sequences have the linear complexity nearly close to their periods
In this paper, for positive integers m, M , and a prime p such that M |p m − 1, we derive linear complexity over the prime field Fp of M-ary Sidel'nikov sequences of period p m −1 using discrete Fourier transform. As a special case, the linear complexity of the ternary Sidel'nikov sequence is presented. It turns out that the linear complexity of a ternary… (More)
— 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 . For p ≡ 1 mod 5, we have obtained the simple closed-form expression of the cyclotomic numbers of order 5 over Fpn. For p ≡ 1 mod 5, we express the cyclotomic number of order 5 over Fpn in terms of the… (More)
In this paper, a new family of M-ary sequences of period p<sup>n</sup> −1 is proposed, which has large family size and the good correlation property, that is, the maximum magnitude of their correlation values is upper bounded by 4√p<sup>n</sup> +5.
In this paper, we proposed a new quaternary low correlation zone(LCZ) sequence set with parameters (2(2<sup>n</sup> - 1),M, L, 2). The new LCZ sequence set is constructed from the binary sequence with ideal autocorrelation of period 2<sup>n</sup> - 1. The proposed construction method corresponds to the generalization of the construction method of binary LCZ… (More)
In this paper, a new family of <i>M</i> -ary sequences of period <i>p</i><sup>n</sup> -1 is proposed. The proposed family is constructed by the addition of cyclic shifts of an <i>M</i> -ary Sidel'nikov sequence and its reverse sequence. The number of sequences contained in this family is about (<i>M</i>-1)<sup>2</sup> times of their period and the maximum… (More)