A001380 Weight distribution of binary Golay code of length 24.
1, 0, 759, 2576, 759, 0, 1
Offset: 0
Examples
The weight enumerator is x^24+759*x^16*y^8+2576*x^12*y^12+759*x^8*y^16+y^24.
References
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 84.
- W. Ebeling, Lattices and Codes, Vieweg; 2nd ed., 2002, see p. 71.
- F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 67.
Links
- J. H. Conway and N. J. A. Sloane, Orbit and coset analysis of the Golay and related codes, IEEE Trans. Inform. Theory, 36 (1990), 1038-1050.
- E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).
Programs
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Maple
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));