Cardinal rank metric codes over Galois rings |
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| Institution: | 1. Universidad del País Vasco - Euskal Herriko Unibertsitatea, 48940 Leioa, Bizkaia, Spain;2. Departamento de Matemáticas, Universidad de Oviedo, 33007 Oviedo, Asturias, Spain;1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy;2. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy |
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| Abstract: | In 1985, Gabidulin introduced the rank metric in coding theory over finite fields, and used this kind of codes in a McEliece cryptosystem, six years later. In this paper, we consider rank metric codes over Galois rings. We propose a suitable metric for codes over such rings, and show its main properties. With this metric, we define Gabidulin codes over Galois rings, propose an efficient decoding algorithm for them, and hint their cryptographic application. |
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| Keywords: | Rank metric codes Error-correcting codes McEliece cryptosystem |
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