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Weight distribution of [12,6,6]_3 ternary extended Golay code.
3

%I #6 Sep 08 2022 08:45:17

%S 1,0,264,440,24

%N Weight distribution of [12,6,6]_3 ternary extended Golay code.

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

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.

%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

%e Weight enumerator is x^12 + 264*x^6*y^6 + 440*x^3*y^9 + 24*y^12.

%o (Magma) K:=FiniteField(3); C:=GolayCode(K,true); W<x,y>:=WeightEnumerator(C); W;

%Y Cf. A105676, A001380, A002289, A105684, A109141.

%K nonn,fini,full

%O 0,3

%A _N. J. A. Sloane_, May 06 2005