A201472 The Griesmer lower bound q_4(5,n) on the length of a linear code over GF(4) of dimension 5 and minimal distance n.

5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 68, 69, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 86, 90, 91, 92, 93, 95, 96, 97, 98, 100, 101, 102, 103, 105, 106, 107, 108, 111, 112, 113, 114, 116, 117, 118, 119, 121, 122, 123, 124, 126, 127, 128, 129, 132, 133, 134, 135

Offset

1,1

References

Bouyukliev, Iliya; Grassl, Markus; and Varbanov, Zlatko; New bounds for n_4(k,d) and classification of some optimal codes over GF(4). Discrete Math. 281 (2004), no. 1-3, 43-66.

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1977, Chap. 17, Section 5.

Links

Table of n, a(n) for n=1..100.

Formula

The Griesmer bound for codes over GF(q) is g_q(k,d) = Sum_{i=0..k-1} ceiling(d/q^i), where k is the dimension and d is the minimal distance.

Maple

g:=(q, k, d)->add( ceil(d/q^i), i=0..k-1);
s:=(q, k)->[seq(g(q, k, d), d=1..100)];
s(4, 5);

Crossrefs

Cf. A201512.

Sequence in context: A088721 A325435 A288857 * A005049 A128427 A292917

Adjacent sequences: A201469 A201470 A201471 * A201473 A201474 A201475

Keyword

nonn

Author

N. J. A. Sloane, Dec 02 2011

Status

approved