论文信息 - Strong deviations from randomness in m-sequences based on trinomials

Strong deviations from randomness in m-sequences based on trinomials

The fixed vector of any m-sequence based on a trinomial is explicitly obtained. Local nonrandomness around the fixed vector is analyzed through model-construction and experiments. We conclude that the initial vector near the fixed vector should be avoided.

Makoto Matsumoto | Yoshiharu Kurita

[1] MICHAEL C. WILLETT,et al. Cycle representatives for minimal cyclic codes (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[2] Pierre L'Ecuyer,et al. Efficient and portable combined Tausworthe random number generators , 1990, TOMC.

[3] Staffan A. Fredricsson. Pseudo-randomness properties of binary shift register sequences (Corresp.) , 1975, IEEE Trans. Inf. Theory.

[4] Makoto Matsumoto,et al. Twisted GFSR generators II , 1994, TOMC.

[5] Y. Kurita,et al. Primitive t-Nomials(t=3,5)over GF(2) Whose Degree is a Mersenne Exponent≦44497 , 1991 .

[6] Solomon W. Golomb,et al. Shift Register Sequences , 1981 .

[7] A. Compagner. The hierarchy of correlations in random binary sequences , 1991 .

[8] J. Heringa,et al. New Primitive Trinomials Of Mersenne-Exponent Degrees For Random-Number Generation , 1992 .

[9] Aaldert Compagner,et al. On the use of reducible polynomials as random number generators , 1993 .

[10] James H. Lindholm. An analysis of the pseudo-randomness properties of subsequences of long m -sequences , 1968, IEEE Trans. Inf. Theory.

[11] Michael Willett. Characteristic $m$-sequences , 1976 .