A030507 Graham-Sloane-type lower bound on the size of a ternary (n,3,7) constant-weight code.

9, 61, 243, 732, 1837, 4056, 8136, 15149, 26571, 44374, 71125, 110094, 165376, 242014, 346136, 485103, 667662, 904109, 1206463, 1588650, 2066688, 2658897, 3386099, 4271843, 5342629, 6628148, 8161525, 9979578, 12123079, 14637028

Offset

7,1

Links

Robert Israel, Table of n, a(n) for n = 7..10000

Patric R. J. Östergård, Mattias Svanström, Ternary Constant Weight Codes, The Electronic Journal of Combinatorics, Volume 9 (2002), Research Paper #R41.

M. Svanström, A lower bound for ternary constant weight codes, IEEE Trans. on Information Theory, Vol. 43, pp. 1630-1632, Sep. 1997.

Mattias Svanström, A Class of Perfect Ternary Constant-Weight Codes, Designs, Codes and Cryptography, Volume 18, Issue 1-3 , pp 223-229.

Formula

a(n) = ceiling (binomial (n, w) * 2^w / (2*n + 1)) for w = 7.

Maple

A:= n -> ceil(binomial(n, 7)*2^7/(2*n+1)):
map(A, [$7 .. 60]); # Robert Israel, Jun 22 2015

Crossrefs

Sequence in context: A159037 A138589 A058777 * A172208 A202660 A202120

Adjacent sequences: A030504 A030505 A030506 * A030508 A030509 A030510

Keyword

nonn

Author

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

Extensions

Formula edited by Robert Israel, Jun 22 2015

Status

approved