A109141
G.f.: fourth root of Hamming weight enumerator of [12,6,6]_3 ternary extended Golay code (cf. A105683).
Original entry on oeis.org
1, 0, 66, 110, -6528, -21780, 986898, 5029200, -173972160, -1211972300, 33051614904, 297628438800, -6538730283946, -73793338948560, 1321581552446628, 18387553507364580, -269415270699505128, -4592418987961074600, 54819166320379762180, 1147693439998612940400
Offset: 0
1+66*x^2+110*x^3-6528*x^4-21780*x^5+986898*x^6+5029200*x^7-...
A105676
Highest minimal Hamming distance of any Type 3 ternary self-dual code of length 4n.
Original entry on oeis.org
3, 3, 6, 6, 6, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18
Offset: 1
The [12,6,6]_3 ternary Golay code has d=6, so a(3) = 6.
- F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.
- P. Gaborit, Tables of Self-Dual Codes
- W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Applic., 11 (2005), 451-490.
- G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
- E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998; (Abstract, pdf, ps).
The sequence continues: a(17) = either 15 or 18, a(18) = 18, ...
A105684
Weight distribution of [11,6,5]_3 ternary Golay perfect code.
Original entry on oeis.org
1, 0, 0, 0, 0, 132, 132, 0, 330, 110, 0, 24
Offset: 0
Weight enumerator is x^11 + 132*x^6*y^5 + 132*x^5*y^6 + 330*x^3*y^8 + 110*x^2*y^9 + 24*y^11.
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag.
- F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977.
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