Geodesic
On vectors of minimal support in transitive linear spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 960-966 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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     title = {On vectors of minimal support in transitive linear spaces},
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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