Some new non-additive maximum rank distance codes |
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Institution: | Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey |
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Abstract: | In this paper, a construction of maximum rank distance (MRD) codes as a generalization of generalized Gabidulin codes is given. The family of the resulting codes is not covered properly by additive generalized twisted Gabidulin codes, and does not cover all twisted Gabidulin codes. When the basis field has more than two elements, this family includes also non-affine MRD codes, and such codes exist for all parameters. Therefore, these codes are the first non-additive MRD codes for most of the parameters. |
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Keywords: | Rank metric codes Maximum rank distance (MRD) codes Additive generalized twisted Gabidulin codes Linearized polynomials |
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