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A new lower bound for the football pool problem for $7$ matches

Laurent Habsieger (1996)

Journal de théorie des nombres de Bordeaux

Let $K_{3} (7, 1)$ denote the minimum cardinality of a ternary code of length $7$ and covering radius one. In a previous paper, we improved on the lower bound $K_{3} (7, 1) \geq 147$ by showing that $K_{3} (7, 1) \geq 150$ . In this note, we prove that $K_{3} (7, 1) \geq 153$ .

A new table of constant weight codes of length greater than 28.

Smith, D.H., Hughes, L.A., Perkins, S. (2006)

The Electronic Journal of Combinatorics [electronic only]

An asymptotic Gilbert-Varshamov bound for $(T, M, S)$ -nets.

Bierbrauer, Jürgen, Schmid, Wolfgang Ch. (2005)

Integers

An Improvement to the Achievement of the Griesmer Bound

Hamada, Noboru, Maruta, Tatsuya (2010)

Serdica Journal of Computing

We denoted by nq(k, d), the smallest value of n for which an [n, k, d]q code exists for given q, k, d. Since nq(k, d) = gq(k, d) for all d ≥ dk + 1 for q ≥ k ≥ 3, it is a natural question whether the Griesmer bound is attained or not for d = dk , where gq(k, d) = ∑[d/q^i], i=0,...,k-1, dk = (k − 2)q^(k−1) − (k − 1)q^(k−2). It was shown by Dodunekov [2] and Maruta [9], [10] that there is no [gq(k, dk ), k, dk ]q code for q ≥ k, k = 3, 4, 5 and for q ≥ 2k − 3, k ≥ 6. The purpose of this paper...

Bounds for digital nets and sequences

Wolfgang Ch. Schmid, Reinhard Wolf (1997)

Acta Arithmetica

Bounds for DNA codes with constant GC-content.

King, Oliver D. (2003)

The Electronic Journal of Combinatorics [electronic only]

Codes that attain minimum distance in every possible direction

Gyula Katona, Attila Sali, Klaus-Dieter Schewe (2008)

Open Mathematics

The following problem motivated by investigation of databases is studied. Let $𝒞$ be a q-ary code of length n with the properties that $𝒞$ has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.