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A binary m-sequence: expansion of reciprocal of x^7 + x^6 + 1.
1

%I #34 Jun 24 2017 13:17:25

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

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

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

%N A binary m-sequence: expansion of reciprocal of x^7 + x^6 + 1.

%C Sequence is 127-periodic. - _Ray Chandler_, Jun 24 2017

%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 Joris Van Kerrebrouck, <a href="/A011686/b011686.txt">Table of n, a(n) for n = 0..126</a>

%H <a href="/index/Rec#order_127">Index entries for linear recurrences with constant coefficients</a>, order 127.

%F a(n) = a(n+127). - _Gheorghe Coserea_, Jun 15 2017

%o (MATLAB)

%o Feedback_shiftregister =[1,1,0,0,0,0,0]; % x^7 + x^6 (+1)

%o sequence = [0 0 0 0 0 0 1]; % start sequence

%o for i = 1:127-7

%o sequence(i+7)=mod(Feedback_shiftregister*sequence(i:i+6)',2)

%o end % _Joris Van Kerrebrouck_, Jun 13 2017

%K nonn

%O 0,1

%A _N. J. A. Sloane_