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Fundam. Prikl. Mat., 2008, Volume 14, Issue 4, Pages 181–192 (Mi fpm1133)  

Pseudogeometries with clusters and an example of a recursive $[4,2,3]_{42}$-code

V. T. Markov, A. A. Nechaev, S. Skazhenik, E. O. Tveritinov

M. V. Lomonosov Moscow State University

Abstract: In 1998, E. Couselo, S. Gonzalez, V. Markov, and A. Nechaev defined the recursive codes and obtained some results that allowed one to conjecture the existence of recursive MDS-codes of dimension 2 and length 4 over any finite alphabet of cardinality $q\notin\{2,6\}$. This conjecture remained open only for $q\in\{14,18,26,42\}$. It is shown in this paper that there exist such codes for $q=42$. We used a new construction, that of pseudogeometry with clusters.

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English version:
Journal of Mathematical Sciences (New York), 2009, 163:5, 563–571

Bibliographic databases:

UDC: 512.548.7+519.143+514.146.5

Citation: V. T. Markov, A. A. Nechaev, S. Skazhenik, E. O. Tveritinov, “Pseudogeometries with clusters and an example of a recursive $[4,2,3]_{42}$-code”, Fundam. Prikl. Mat., 14:4 (2008), 181–192; J. Math. Sci., 163:5 (2009), 563–571

Citation in format AMSBIB
\Bibitem{MarNecSka08}
\by V.~T.~Markov, A.~A.~Nechaev, S.~Skazhenik, E.~O.~Tveritinov
\paper Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 4
\pages 181--192
\mathnet{http://mi.mathnet.ru/fpm1133}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2482041}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 163
\issue 5
\pages 563--571
\crossref{https://doi.org/10.1007/s10958-009-9694-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70649112121}


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  • Фундаментальная и прикладная математика
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