Geodesic
On the covering radius of the linear codes generated by the affine geometries over $\mathrm{GF}(4)$
Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 72-77
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The covering radius for a code is defined to be a maximal distance between a space vector and the code. It is shown that the covering radius for a linear code generated by the affine geometry over $\mathrm{GF}(4)$ equals 4.
Keywords: linear codes, finite affine geometries, covering radius. 
@article{PDM_2014_4_a7,
     author = {M. E. Kovalenko},
     title = {On the covering radius of the linear codes generated by the affine geometries over~$\mathrm{GF}(4)$},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {72--77},
     year = {2014},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_4_a7/}
}
TY  - JOUR
AU  - M. E. Kovalenko
TI  - On the covering radius of the linear codes generated by the affine geometries over $\mathrm{GF}(4)$
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2014
SP  - 72
EP  - 77
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/PDM_2014_4_a7/
LA  - ru
ID  - PDM_2014_4_a7
ER  - 
%0 Journal Article
%A M. E. Kovalenko
%T On the covering radius of the linear codes generated by the affine geometries over $\mathrm{GF}(4)$
%J Prikladnaâ diskretnaâ matematika
%D 2014
%P 72-77
%N 4
%U http://geodesic.mathdoc.fr/item/PDM_2014_4_a7/
%G ru
%F PDM_2014_4_a7
M. E. Kovalenko. On the covering radius of the linear codes generated by the affine geometries over $\mathrm{GF}(4)$. Prikladnaâ diskretnaâ matematika, no. 4 (2014), pp. 72-77. http://geodesic.mathdoc.fr/item/PDM_2014_4_a7/

[1] Mak-Vilyams F. Dzh., Sloen N. Dzh., Teoriya kodov, ispravlyayuschikh oshibki, Svyaz, M., 1979

[2] Cohen G., Honkala I., Litsyn S., Lobstein A., Covering Codes, Elsevier, North Holland, 1997 | MR | Zbl

[3] Kovalenko M. E., Urbanovich T. A., “O range matrits intsidentnosti tochek i pryamykh konechnykh affinnykh i proektivnykh geometrii nad polem iz chetyrekh elementov”, Problemy peredachi informatsii, 50:1 (2014), 87–97 | MR

[4] Reid C., Rosa A., “Steiner systems $S(2,4,v)$ – a survey”, Electronic J. Combinatorics, 2010, #DS18, 34 pp. http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS18 | Zbl

[5] Tarannikov Yu. V., “O rangakh podmnozhestv prostranstva dvoichnykh vektorov, dopuskayuschikh vstraivanie sistemy Shteinera $S(2,4,v)$”, Prikladnaya diskretnaya matematika, 2014, no. 1, 73–76