FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 4, PAGES 181-192

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

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

Abstract

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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 $q$Ï {2,6}. This conjecture remained open only for $q$Î {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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Last modified: February 26, 2009