Related papers: Extended Gabidulin-Kronecker Product Codes and The…
Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet…
Constant dimension codes (CDCs), as special subspace codes, have received a lot of attention due to their application in random network coding. This paper introduces a family of new codes, called rank metric codes with given ranks (GRMCs),…
Recent work has shown that properly designed protograph-based LDPC codes may have minimum distance linearly increasing with block length. This notion rests on ensemble arguments over all possible expansions of the base protograph. When…
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…
This article defines multi-twisted Goppa (MTG) codes as subfield subcodes of duals of multi-twisted Reed-Solomon (MTRS) codes and examines their properties. We show that if $t$ is the degree of the MTG polynomial defining an MTG code, its…
Orthogonal geometric constructions are the basis of many many quantum error-correcting codes (QEC), but strict orthogonality constraints limit design flexibility and resource efficiency. We introduce a quasi-orthogonal geometric framework…
This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps taken to perform the Generalized Minimum Distance decoding are similar…
Constant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for nearly sixty years. In this paper we show that for {\it…
Encryption schemes based on the rank metric lead to small public key sizes of order of few thousands bytes which represents a very attractive feature compared to Hamming metric-based encryption schemes where public key sizes are of order of…
Cyclic redundancy check (CRC) codes combined with convolutional codes yield a powerful concatenated code that can be efficiently decoded using list decoding. To help design such systems, this paper presents an efficient algorithm for…
In the realm of rank-metric codes, Maximum Rank Distance (MRD) codes are optimal algebraic structures attaining the Singleton-like bound. A major open problem in this field is determining whether an MRD code can be extended to a longer one…
Rank Quasi-Cyclic Signature (RQCS) is a rank metric code-based signature scheme based on the Rank Quasi-Cyclic Syndrome Decoding (RQCSD) problem proposed by Song et al. in [2]. Their paper was accepted in the 22nd International Conference…
In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
We give a construction of quantum LDPC codes of dimension $\Theta(\log N)$ and distance $\Theta(N/\log N)$ as the code length $N\to\infty$. Using a product of chain complexes this construction also provides a family of quantum LDPC codes of…
The iteration complexity of the block-coordinate descent (BCD) type algorithm has been under extensive investigation. It was recently shown that for convex problems the classical cyclic BCGD (block coordinate gradient descent) achieves an…
Quantum key distribution (QKD) allows the generation of cryptographic keys beyond the computational hardness paradigm and is befitting for secure data transmission requiring long-term security. The communication distance of fibre-based QKD,…
Reference-frame-independent (RFI) quantum key distribution (QKD) presents promising advantages, especially for mobile-platform-based implementations, as it eliminates the need for active reference frame calibration. While RFI-QKD has been…
We propose a maximum toroidal distance (MTD) code for lattice-based public-key encryption (PKE). By formulating the encryption encoding problem as the selection of $2^\ell$ points in the discrete $\ell$-dimensional torus…
New near-capacity continuous-variable quantum key distribution (CV-QKD) reconciliation schemes are proposed, where both the authenticated classical channel (ClC) and the quantum channel (QuC) for QKD are protected by separate forward error…