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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