Construction of linear codes with prescribed minimum distance
نویسندگان
چکیده
We construct linear codes over finite fields with prescribed minimum distance by selectiong columns of the generator matrix. This selection problem can be formulated as an integer programming problem. In order to reduce the search space we prescribe a group of automorphisms. Then, in many cases the resulting integer programming problem can be solved by lattice point enumeration. With this approach numerous known lower bounds on the minimum distance of linear codes could be improved. In the special case of projective q-ary [n, 3, d] codes we get (n, n− d)-arcs over PG(2, q).
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