On decoding additive generalized twisted Gabidulin codes

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 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.

Encoding and Decoding of Several Optimal Rank Metric Codes

“…, fn−1 ) and M T l is the transpose of the matrix M l . When n, d are integers with opposite parities as shown in (10), only the first κ and the last κ elements of f are non zero. Also in the case when n, d are both odd integers, as can be seen in ( 12), the first m − κ and the last m − κ − 2 elements of f are zero.…”

“…Known decoding algorithms for MRD codes can be generally classified in two different approaches: syndrome-based decoding as in [5,7,25,27] and interpolation-based decoding as in [9,10,13,14,16,24]. Gabidulin in [5] solves the key equation in the decoding process by employing the linearized version of extended Euclidean (LEE) algorithm, while in [25], the key equation was solved by a linearized version of Berlekamp-Massey (BM) algorithm.…”

“…Later this idea was adopted to decode additive generalized twisted Gabidulin codes and Trombetti-Zhou rank metric codes [10,11]. Again BM algorithm is involved in the process of solving the key equations in [10] and [11] and it reduces the decoding problem to the problem of solving the projective polynomial equation x q v +1 + ax + b = 0 and quadratic polynomial equation x 2 +cx+d = 0 over F q n , respectively. A similar idea is also used in [9] to decode Gabidulin codes beyond half the minimum distance.…”

Hermitian Rank Metric Codes and Duality

“…Additive codes and self-duality are also considered in the ambient space of matrices endowed with the rank metric (see, for example, [22], [25], [26]). They have potential applications not only in network coding, combinatorics and cryptography but also in code-based cryptography (and hence post-quantum cryptography).…”

New Communication Models and Decoding of Maximum Rank Distance Codes

“…Randrianarisoa in [15] gave an interpolation-based decoding algorithm for Gabidulin codes and also for GTG codes. This idea is used later in [21], [22], [23] and [24] to decode AGTG [7], Non-additive partition MRD codes [25], TZ codes [8] and Hermitain Rank metric codes [26], respectively.…”