Geodesic
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/}
}
TY  - JOUR
AU  - Hamada, Noboru
AU  - Maruta, Tatsuya
TI  - An Improvement to the Achievement of the Griesmer Bound
JO  - Serdica Journal of Computing
PY  - 2010
SP  - 301
EP  - 320
VL  - 4
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2010_4_3_a1/
LA  - en
ID  - SJC_2010_4_3_a1
ER  - 
%0 Journal Article
%A Hamada, Noboru
%A Maruta, Tatsuya
%T An Improvement to the Achievement of the Griesmer Bound
%J Serdica Journal of Computing
%D 2010
%P 301-320
%V 4
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2010_4_3_a1/
%G en
%F 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/