A030509 Graham-Sloane-type lower bound on the size of a ternary (n,3,9) constant-weight code.

27, 244, 1225, 4506, 13559, 35346, 82664, 177494, 355621, 672796, 1212758, 2097452, 3499818, 5659535, 8902155, 13662083, 20509867, 30184333, 43630080, 62040927, 86909874, 120086243, 163840610, 220938240, 294721720, 389203523, 509169290, 660292594, 849262046

Offset

9,1

Links

Table of n, a(n) for n=9..37.

Mattias Svanstrom, A lower bound for ternary constant weight codes, IEEE Trans. on Information Theory, Vol. 43 (Sep. 1997), pp. 1630-1632.

Formula

a(n) = ceiling(binomial(n, w) * 2^w / (2*n + 1)) with w = 9.

Mathematica

a[n_] := Ceiling[Binomial[n, 9] * 2^9 / (2*n + 1)]; Array[a, 40, 9] (* Amiram Eldar, Oct 31 2025 *)

Crossrefs

Column k=9 of A390161.

Sequence in context: A075548 A345054 A074117 * A042414 A099226 A016107

Adjacent sequences: A030506 A030507 A030508 * A030510 A030511 A030512

Keyword

nonn,easy

Author

Mattias Svanstrom (mattias(AT)isy.liu.se)

Status

approved