A011743 A binary m-sequence: expansion of reciprocal of x^30 + x^16 + x^15 + x + 1 (mod 2, shifted by 29 initial 0's).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Periodic with length of period 2^30-1. - M. F. Hasler, Feb 17 2018

References

• S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
• H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
• F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

Crossrefs

Cf. A011655, A011656, ..., A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).

Programs

PARI

A011743_vec=concat([1..29]*0, Vec(1/(x^30+x^16+x^15+x+1)+O(x^99))%2)
A=matrix(30, 30, i, j, if(i>1, i==j+1, setsearch([1,15,16,30], j)>0))*Mod(1, 2);
A011743(n)=lift((A^(n-29))[1, 1]) \\ M. F. Hasler, Feb 17 2018