A006006 Weight distribution of [ 128,29,32 ] 2nd-order Reed-Muller code.

1, 0, 0, 0, 10668, 0, 5291328, 112881664, 300503590, 112881664, 5291328, 0, 10668, 0, 0, 0, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Examples

			x^128+10668*x^96*y^32+5291328*x^80*y^48+112881664*x^72*y^56+300503590*x^64*y^64+112881664*x^56*y^72+5291328*x^48*y^80+10668*x^32*y^96+y^128
The weight distribution is:
i A_i
0 1
32 10668
48 5291328
56 112881664
64 300503590
72 112881664
80 5291328
96 10668
128 1
		

References

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

Links

• E. R. Berlekamp and N. J. A. Sloane, Weight Enumerator for Second-Order Reed-Muller Codes, IEEE Trans. Information Theory, IT-16 (1970), 745-751.
• Claude Carlet and Patrick Solé, The weight spectrum of several families of Reed-Muller codes, arXiv:2301.13497 [cs.IT], 2023.
• S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
• M. Terada, J. Asatani and T. Koumoto, Weight Distribution

Programs

Magma

R := ReedMullerCode(2,7); W := WeightEnumerator(R); W;