Quasi-uniform codes and their applications
Date
2013
Authors
Chan, T.H.
Grant, A.
Britz, T.
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Journal article
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IEEE Transactions on Information Theory, 2013; 59(12, article no. 6589163):7915-7926
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Quasi-uniform random vectors have probability distributions that are uniform over their projections. They are of fundamental interest because a linear information inequality is valid if and only if it is satisfied by all quasi-uniform random vectors. In this paper, we investigate properties of codes induced by quasi-uniform random vectors. We prove that quasi-uniform codes (which include linear and almost affine codes as special cases) are distance-invariant and that Greeneās Theorem and the Critical Theorem of Crapo and Rota hold in the setting of quasi-uniform codes. We show that both theorems are essentially combinatorial but not algebraical in nature. Linear programming bounds proposed by Delsarte are extended for quasi-uniform codes.
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Copyright 2013 IEEE