Rank-Metric Codes Over Finite Principal Ideal Rings and Applications

2019 ◽  
Vol 65 (12) ◽  
pp. 7718-7735 ◽  
Author(s):  
Hermann Tchatchiem Kamche ◽  
Christophe Mouaha
Keyword(s):  
Principal Ideal ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
Finite Principal Ideal Rings

scholarly journals Generalization of low rank parity-check (LRPC) codes over the ring of integers modulo a positive integer

2021 ◽  
Author(s):  
Franck Rivel Kamwa Djomou ◽  
Hervé Talé Kalachi ◽  
Emmanuel Fouotsa
Keyword(s):  
International Workshop ◽  
Low Rank ◽  
Parity Check ◽  
Chain Ring ◽  
Ring Of Integers ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
A Chain ◽  
Finite Principal Ideal Rings ◽  
Ieee International Symposium

AbstractFollowing the work of Gaborit et al. (in: The international workshop on coding and cryptography (WCC 13), 2013) defining LRPC codes over finite fields, Renner et al. (in: IEEE international symposium on information theory, ISIT 2020, 2020) defined LRPC codes over the ring of integers modulo a prime power, inspired by the paper of Kamche and Mouaha (IEEE Trans Inf Theory 65(12):7718–7735, 2019) which explored rank metric codes over finite principal ideal rings. In this work, we successfully extend the work of Renner et al. by constructing LRPC codes over the ring $$\mathbb {Z}_{m}$$ Z m which is not a chain ring. We give a decoding algorithm and we study the failure probability of the decoder.

On interleaved rank metric codes

2020 ◽  
Author(s):  
Vladimir Sidorenko ◽  
Wenhui Li ◽  
Gerhard Kramer
Keyword(s):  
Rank Metric ◽  
Rank Metric Codes

scholarly journals Rank-metric codes and q-polymatroids

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

scholarly journals Several classes of optimal Ferrers diagram rank-metric codes

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

scholarly journals Tensor Representation of Rank-Metric Codes

2019 ◽  
Vol 3 (4) ◽  
pp. 614-643
Author(s):  
Eimear Byrne ◽  
Alessandro Neri ◽  
Alberto Ravagnani ◽  
John Sheekey
Keyword(s):  
Tensor Representation ◽  
Rank Metric ◽  
Rank Metric Codes

scholarly journals Rank-Metric Codes, Generalized Binomial Moments and their Zeta Functions

2020 ◽  
Vol 604 ◽  
pp. 92-128
Author(s):  
Eimear Byrne ◽  
Giuseppe Cotardo ◽  
Alberto Ravagnani
Keyword(s):  
Zeta Functions ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
Binomial Moments
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