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Codes and noncommutative stochastic matrices

Sylvain Lavallée 1 Christophe Reutenauer 2 Vladimir Retakh 3 Dominique Perrin 4
1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]
3 Department of Mathematics - Rutgers School of Arts and Sciences
4 LIGM - Laboratoire d'Informatique Gaspard-Monge
Abstract : Given a matrix over a skew field fixing the column t(1,...,1), we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes.
Mots-clés : stochastic matrices codes eigenvectors quasi-determinants
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Sylvain Lavallée, Christophe Reutenauer, Vladimir Retakh, Dominique Perrin. Codes and noncommutative stochastic matrices. Journal of Noncommutative Geometry, European Mathematical Society, 2010, 4 (4), pp.531-554. ⟨10.4171/JNCG/65⟩. ⟨hal-00793906⟩

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