Geodesic
On vectors of minimal support in transitive linear spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 960-966.

Voir la notice de l'article provenant de la source Math-Net.Ru

We discuss the minimum distance problem of some transitive linear spaces. A minimal support of vectors in monogenerated coordinate-transitive spaces problem is solved for ones generated by a vector of weight 2. In the case of generating vector of weight 3 some conjectures are provided by computer experiments. Attainable lower bound on the support cardinality with respect to dimension of linear space is obtained. Also a connection between full-rank criterion for vector and tilings of groups is mentioned.
Keywords: transitive linear spaces, support of a vector, minimum distance problem.
Mots-clés : code distance 
@article{SEMR_2015_12_a58,
     author = {S. V. Avgustinovich and O. G. Parshina},
     title = {On vectors of minimal support in transitive linear spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {960--966},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a58/}
}
TY  - JOUR
AU  - S. V. Avgustinovich
AU  - O. G. Parshina
TI  - On vectors of minimal support in transitive linear spaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 960
EP  - 966
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a58/
LA  - ru
ID  - SEMR_2015_12_a58
ER  - 
%0 Journal Article
%A S. V. Avgustinovich
%A O. G. Parshina
%T On vectors of minimal support in transitive linear spaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 960-966
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a58/
%G ru
%F SEMR_2015_12_a58
S. V. Avgustinovich; O. G. Parshina. On vectors of minimal support in transitive linear spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 960-966. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a58/

[1] A. Vardy, “Algoritmic complexity in coding theory and the minimum distance problem”, STOC '97 (El Paso, TX), ACM, New York, 1999, 92–109 (electronic) | MR | Zbl

[2] E. R. Berlekamp, R. J. McEliece, H. C. A. van Tilborg, “On the inherent intractability of certain coding problems”, IEEE Trans. Inform. Theory, 24 (1978), 384–386 | DOI | MR | Zbl

[3] D. M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs. Theory and Application, Second edition, VEB Deutscher Verlag der Wissenschaften, Berlin, 1982, 368 pp. | MR

[4] M. Dinitz, “Full rank tilings of finite abelian groups”, SIAM J. Discrete Math., 20 (2006), 160–170 | DOI | MR | Zbl

[5] D. K. Zhukov, “Tilings of $p$-ary cyclic groups”, Siberian Electronic Mathematical Reports, 10 (2013), 562–565 | MR | Zbl