Codes and Noncommutative Stochastic Matrices
Sylvain Lavall\'ee, Christophe Reutenauer, Vladimir Retakh, Dominique, Perrin
TL;DR
This paper develops formulas for fixed vectors of matrices over skew fields and extends probabilistic properties of codes into the noncommutative setting, advancing algebraic and coding theory.
Contribution
It introduces noncommutative extensions of probabilistic properties of codes and provides formulas for fixed vectors of matrices over skew fields.
Findings
Formulas for fixed vectors over skew fields.
Noncommutative probabilistic properties of codes.
Extension of classical coding theory into noncommutative algebra.
Abstract
Given a matrix over a skew field fixing the column (1,...,1)^t, 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.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Random Matrices and Applications