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In this paper, a new construction method of quaternary sequences of even period 2N having the ideal autocorrelation and balance properties is proposed. These quaternary sequences are constructed by applying the inverse Gray mapping to binary sequences of odd period N with the ideal autocorrelation. Autocorrelation distribution of the proposed quaternary… (More)
In this paper, for an integer k, we evaluate an upper bound for the cross-correlation of a ternary m-sequence of period N = 3 − 1 and its decimated sequence with decimation d = 3 −3+2 4 +3. It is found that the cross-correlation is upper bounded by 4.5 · 3 + 1.
For a prime p ≡ 1 mod 4, an odd integer n, and d = p<sup>n</sup>+1 over p+1 + p<sup>n</sup>−1 over 2, we investigate the cross-correlation values of p-ary m-sequence m(t) of period p<sup>n</sup> − 1 and its decimated m-sequence m(dt). It is shown that the cross-correlation function between m(t) and m(dt) takes the values in equation.
In this paper, we derive the cyclotomic numbers of order 5 over an extension field F<sub>p</sub> <sup>n</sup> using the well-known results of quintic Jacobi sums over F<sub>p</sub> (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 F<sub>p</sub> <sup>n</sup>. For p… (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, the relationship among -ary Sidel'nikov sequences generated by different primitive elements and decimation are studied. Their autocorrelation function and autocorrelation distribution are derived. It is proved that Sidel'nikov sequences for a given period are equivalent under the decimation, cyclic shift, and scalar multiplication of the… (More)