Abstract
In this paper, we consider an interpolation-based decoding algorithm for a large family of maximum rank distance codes, known as the additive generalized twisted Gabidulin codes, over the finite field mathbb {F}_{q^{n}} for any prime power q. This paper extends the work of the conference paper Li and Kadir (2019) presented at the International Workshop on Coding and Cryptography 2019, which decoded these codes over finite fields in characteristic two.
Highlights
Error correction codes with the rank metric have found applications in space-time coding [27], random network coding [44] and cryptography [12]
In [20, 39], the Frobenious automorphism in the Gabidulin codes were generalized to arbitrary automorphism and generalized Gabidulin (GG) codes
The known decoding algorithms for Gabidulin codes cannot be directly applied to those new maximum rank distance (MRD) codes with twisted evaluation polynomials, especially when the MRD codes are only linear over the ground field Fq or its subfield
Summary
Error correction codes with the rank metric have found applications in space-time coding [27], random network coding [44] and cryptography [12]. Using the same idea for generalizing Gabidulin codes, arbitrary automorphism was employed to construct generalized twisted Gabidulin (GTG) codes This family of MRD codes were first described in [40, Remark 9] and later comprehensively studied in [26]. The known decoding algorithms for Gabidulin codes cannot be directly applied to those new MRD codes with twisted evaluation polynomials, especially when the MRD codes are only linear over the ground field Fq or its subfield. Randrianarisoa later proposed an interpolation approach to decoding twisted Gabidulin codes in [35] , where he gave a brief discussion on the case when the rank of the error vector reaches the unique error-correcting radius of the twisted Gabidulin codes.
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