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Computation of weight enumerators of binary linear codes using the package “Coding Theory”

Igor Gachkov
Organization: Karlstad University
Department: Department of Engineering Sciences

2004 International Mathematica Symposium
Conference location

Banff, Canada

Using the package "Coding Theory in Mathematica" illustrates Sidelnikovs theorem: “Some weight distributions of linear codes are asymptotically normal “. We give a simple description of the Wagner code with parameters (23,14,5), and prove that the code is quasi-perfect. We use Mathematica to obtain, using linear programming, a weight distribution of the Wagner code. This method of calculating the weight polynomial allows us to prove the optimum of the Wagner code among the family of codes correcting two errors with nine checking symbols.

*Mathematics > Algebra > Linear Algebra

coding theory, Sidelnikovs theorem, asymptotically normal, Wagner code, weight distribution
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