A085517 Weight enumerator of [16,7,6] extended BCH code.

1, 0, 0, 48, 30, 48, 0, 0, 1

Offset

0,4

Comments

One of the three possible weight distributions for a [16,7,6] binary code.

The interspersed zeros have been omitted.

References

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

J. Simonis, Codes and semilinear spaces, pp. 518-528 of A. Barlotti et al., eds., Combinatorics `90, North-Holland 1992.

Links

Table of n, a(n) for n=0..8.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Example

x^16 + 48*x^10*y^6 + 30*x^8*y^8 + 48*x^6*y^10 + y^16.

Prog

(Magma) C := BCHCode(GF(2), 15, 5); D:=ExtendCode(C); W<x, y>:=WeightEnumerator(D);

Crossrefs

Cf. A085518, A085519, A109475.

Sequence in context: A298451 A094658 A136455 * A299525 A033694 A156461

Adjacent sequences: A085514 A085515 A085516 * A085518 A085519 A085520

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Jul 03 2003

Status

approved