Pseudogeometries with clusters and an example of a recursive $[4,2,3]_{42}$-code
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 181-192
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.
@article{FPM_2008_14_4_a11,
author = {V. T. Markov and A. A. Nechaev and S. Skazhenik and E. O. Tveritinov},
title = {Pseudogeometries with clusters and an example of a~recursive $[4,2,3]_{42}$-code},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {181--192},
year = {2008},
volume = {14},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/}
}
TY - JOUR
AU - V. T. Markov
AU - A. A. Nechaev
AU - S. Skazhenik
AU - E. O. Tveritinov
TI - Pseudogeometries with clusters and an example of a recursive $[4,2,3]_{42}$-code
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2008
SP - 181
EP - 192
VL - 14
IS - 4
UR - http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/
LA - ru
ID - FPM_2008_14_4_a11
ER -
%0 Journal Article
%A V. T. Markov
%A A. A. Nechaev
%A S. Skazhenik
%A E. O. Tveritinov
%T Pseudogeometries with clusters and an example of a recursive $[4,2,3]_{42}$-code
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2008
%P 181-192
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/
%G ru
%F FPM_2008_14_4_a11
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. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 181-192. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a11/
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