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

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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