An Improvement to the Achievement of the Griesmer Bound
Serdica Journal of Computing, Tome 4 (2010) no. 3, pp. 301-320
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
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).
Keywords:
Linear Codes, Griesmer Bound, Projective Geometry
@article{SJC_2010_4_3_a1,
author = {Hamada, Noboru and Maruta, Tatsuya},
title = {An {Improvement} to the {Achievement} of the {Griesmer} {Bound}},
journal = {Serdica Journal of Computing},
pages = {301--320},
publisher = {mathdoc},
volume = {4},
number = {3},
year = {2010},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SJC_2010_4_3_a1/}
}
Hamada, Noboru; Maruta, Tatsuya. An Improvement to the Achievement of the Griesmer Bound. Serdica Journal of Computing, Tome 4 (2010) no. 3, pp. 301-320. http://geodesic.mathdoc.fr/item/SJC_2010_4_3_a1/