scholarly journals Cardinal rank metric codes over Galois rings

2022 ◽  
Vol 77 ◽  
pp. 101946
Author(s):  
Markel Epelde ◽  
Ignacio F. Rúa
Author(s):  
Vladimir Sidorenko ◽  
Wenhui Li ◽  
Gerhard Kramer

Author(s):  
Julian Renner ◽  
Alessandro Neri ◽  
Sven Puchinger

AbstractLow-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over Galois rings—a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.’s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above.


2019 ◽  
Vol 52 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Elisa Gorla ◽  
Relinde Jurrius ◽  
Hiram H. López ◽  
Alberto Ravagnani

2019 ◽  
Vol 581 ◽  
pp. 128-144 ◽  
Author(s):  
Shuangqing Liu ◽  
Yanxun Chang ◽  
Tao Feng

2019 ◽  
Vol 3 (4) ◽  
pp. 614-643
Author(s):  
Eimear Byrne ◽  
Alessandro Neri ◽  
Alberto Ravagnani ◽  
John Sheekey

2020 ◽  
Vol 604 ◽  
pp. 92-128
Author(s):  
Eimear Byrne ◽  
Giuseppe Cotardo ◽  
Alberto Ravagnani

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