Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1596

 Title: An Improvement to the Achievement of the Griesmer Bound Authors: Hamada, NoboruMaruta, Tatsuya Keywords: Linear CodesGriesmer BoundProjective Geometry Issue Date: 2010 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Journal of Computing, Vol. 4, No 3, (2010), 301p-320p Abstract: 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 is to determine nq(k, d) for d = dk as nq(k, d) = gq(k, d) + 1 for q ≥ k with 3 ≤ k ≤ 8 except for (k, q) = (7, 7), (8, 8), (8, 9). URI: http://hdl.handle.net/10525/1596 ISSN: 1312-6555 Appears in Collections: Volume 4 Number 3

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