login
Weight distribution of binary Golay code of length 24.
9

%I #16 Feb 01 2022 01:34:44

%S 1,0,759,2576,759,0,1

%N Weight distribution of binary Golay code of length 24.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 84.

%D W. Ebeling, Lattices and Codes, Vieweg; 2nd ed., 2002, see p. 71.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 67.

%H J. H. Conway and N. J. A. Sloane, <a href="https://www.researchgate.net/publication/3077646_Orbit_and_Coset_Analysis_of_the_Golay_and_Related_Codes">Orbit and coset analysis of the Golay and related codes</a>, IEEE Trans. Inform. Theory, 36 (1990), 1038-1050.

%H E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (<a href="http://neilsloane.com/doc/self.txt">Abstract</a>, <a href="http://neilsloane.com/doc/self.pdf">pdf</a>, <a href="http://neilsloane.com/doc/self.ps">ps</a>).

%e The weight enumerator is x^24+759*x^16*y^8+2576*x^12*y^12+759*x^8*y^16+y^24.

%p g24 := x^24+759*x^16*y^8+759*x^8*y^16+2576*x^12*y^12+y^24; e8 := x^8+14*x^4*y^4+y^8; d:=n->x^(n mod 2)*(1/2)*( (x^2+y^2)^floor((n)/2)+(x^2-y^2)^floor((n)/2));

%Y Cf. A002289, A034414, A034415.

%K nonn,fini,full

%O 0,3

%A _N. J. A. Sloane_