Dual toric codes and polytopes of degree one
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Society for Industrial and Applied Mathematics Publications
We define a statistical measure of the typical size of words of low weight in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are characterized, among all dual toric codes, by being extremal with respect to this measure. We also give a geometric interpretation of the minimum distance of dual toric codes and characterize its extremal values. Finally, we obtain exact formulas for the parameters of both primal and dual toric codes associated to polytopes of degree one. © 2015 Society for Industrial and Applied Mathematics.
Topology , Exact formulas , Finite fields , Geometric interpretation , Linear codes , Minimal degree , Minimum distance , Statistical measures , Toric varieties , Codes (symbols) , Codes over finite fields , Toric varieties , Varieties of minimal degree