Related papers: New algorithms for decoding in the rank metric and…

We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the…

In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…

While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…

McEliece encryption scheme which enjoys relatively small key sizes as well as a security reduction to hard problems of coding theory. Furthermore, it remains secure against a quantum adversary and is very well suited to low cost…

The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently…

In this paper we give a randomized reduction for the Rank Syndrome Decoding problem and Rank Minimum Distance problem for rank codes. Our results are based on an embedding from linear codes equipped with Hamming distance unto linear codes…

Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to list decodability have been completely determined, little work…

In order to understand the performance of a code under maximum-likelihood (ML) decoding, it is crucial to know the minimal codewords. In the context of linear programming (LP) decoding, it turns out to be necessary to know the minimal…

Recently, neural networks have improved MinSum message-passing decoders for low-density parity-check (LDPC) codes by multiplying or adding weights to the messages, where the weights are determined by a neural network. The neural network…

Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…

Low-rank parity-check (LRPC) are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et…

Low-density parity-check (LDPC) codes are one of the most promising families of codes to replace the Goppa codes originally used in the McEliece cryptosystem. In fact, it has been shown that by using quasi-cyclic low-density parity-check…

In this study, we investigate the characteristics of scheduling sequences that enable efficient decoding of generalized low-density parity-check (GLDPC) codes under the layered message-passing algorithm. In particular, we show that…

It is known belief propagation decoding variants of LDPC codes can be unrolled easily as neural networks after assigning differed weights to message passing edges flexibly. In this paper we focus on how to determine these weights, in the…

The Rank Decoding problem (RD) is at the core of rank-based cryptography. This problem can also be seen as a structured version of MinRank, which is ubiquitous in multivariate cryptography. Recently, \cite{BBBGNRT20,BBCGPSTV20} proposed…

The McEliece cryptosystem based on quasi-cyclic moderate-density parity-check (QC-MDPC) codes is first purposed in 2013\cite{QCMDPC} and is considered a promising contender in the post-quantum era. Understanding its security is hence…

We propose and analyze an interleaved variant of Loidreau's rank-metric cryptosystem based on rank multipliers. We analyze and adapt several attacks on the system, propose design rules, and study weak keys. Finding secure instances requires…

In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition.…

This is a chapter of the upcoming "A Concise Encyclopedia of Coding Theory", W.C. Huffman, J.-L. Kim, and P. Sole' Eds., CRC Press. The chapter gives an introduction to the mathematical theory of rank-metric codes. Treated topics include:…

A new protograph-based framework for message passing (MP) decoding of low density parity-check (LDPC) codes with Hamming weight amplifiers (HWAs), which are used e.g. in the NIST post-quantum crypto candidate LEDAcrypt, is proposed. The…