Related papers: Several Classes of Concatenated Quantum Codes: Con…
In this work we investigate unions of lifted MRD codes of a fixed dimension and minimum distance and derive an explicit formula for the cardinality of such codes. This will then imply a lower bound on the cardinality of constant dimension…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
Series of maximum distance quantum error-correcting codes are developed and analysed. For a given rate and given error-correction capability, quantum error-correcting codes with these specifications are constructed. The codes are explicit…
A novel code construction based on spatially coupled low-density parity-check (SC-LDPC) codes is presented. The proposed code ensembles are described by protographs, comprised of several protograph-based chains characterizing individual…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…
This paper studies on the cardinality of perfect multi deletion binary codes. The lower bound for any perfect deletion code with the fixed code length and the number of deletions, and the asymptotic achievable of Levenshtein's upper bound…
Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and…
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are…
Multi-twisted (MT) codes were introduced as a generalization of quasi-twisted (QT) codes. QT codes have been known to contain many good codes. In this work, we show that codes with good parameters and desirable properties can be obtained…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
It has been a great challenge to construct new quantum MDS codes. In particular, it is very hard to construct quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known $q$-ary quantum MDS…
We give a new asymptotic upper bound on the size of a code in the Grassmannian space. The bound is better than the upper bounds known previously in the entire range of distances except very large values.
We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than $d$. The achievability argument involves an iterative construction of a set of radius-$d$ balls, each centered at a…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
We provide a construction for quantum codes (hermitian-self-orthogonal codes over GF(4)) starting from cyclic codes over GF(4^m). We also provide examples of these codes some of which meet the known bounds for quantum codes.
Encoding quantum information in a quantum error correction (QEC) code offers protection against decoherence and enhances the fidelity of qubits and gate operations. One of the fundamental challenges of QEC is to construct codes with…
We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
We derive upper bounds on the rate of transmission of classical information over quantum channels by block codes with a given blocklength and error probability, for both entanglement-assisted and unassisted codes, in terms of a unifying…