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A201472
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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.
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0
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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
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OFFSET
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1,1
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REFERENCES
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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.
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LINKS
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FORMULA
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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.
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MAPLE
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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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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