login
A binary m-sequence: expansion of reciprocal of x^27 + x^8 + x^7 + x + 1 (mod 2, shifted by 26 initial 0's).
0

%I #12 Feb 17 2018 15:25:33

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,

%T 0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,

%U 1,1,1,1,1,1,1,0,0,0,0,0,1

%N A binary m-sequence: expansion of reciprocal of x^27 + x^8 + x^7 + x + 1 (mod 2, shifted by 26 initial 0's).

%C Sequence is 2^27-1 = 134217727-periodic. - _M. F. Hasler_, Feb 17 2018

%D S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.

%D H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

%H <a href="/index/Rec#order_134217727">Index entries for linear recurrences with constant coefficients</a>, order 134217727.

%H <a href="/index/Per#periodic">Index entries for periodic sequences with large period</a>.

%F G.f. = x^26/(x^27 + x^8 + x^7 + x + 1) over GF(2). - _M. F. Hasler_, Feb 17 2018

%o (PARI) A=matrix(N=27,N,i,j, if(i>1, i==j+1, setsearch([1,7,8,N],j)>0))*Mod(1, 2); a(n)=lift((A^(n-#A+1))[1,1]) \\ _M. F. Hasler_, Feb 17 2018

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

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E Edited by _M. F. Hasler_, Feb 17 2018