Related papers: Quasi Linear Codes: Application to Point-to-Point …
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…
The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…
In this paper, we show that the projective Reed-Muller~(PRM) codes form a family of locally correctable codes~(LCC) in the regime of low query complexities. A PRM code is specified by the alphabet size $q$, the number of variables $m$, and…
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…
Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further,…
A simple and general definition of quasi cyclic low density parity check (QC LDPC) codes which are constructed based on circulant permutation matrices (CPM) is proposed. As an special case of this definition, we first represent one type of…
Existence of quantum low-density parity-check (LDPC) codes whose minimal distance scales linearly with the number of qubits is a major open problem in quantum information. Its practical interest stems from the need to protect information in…
A linear block code with dimension $k$, length $n$, and minimum distance $d$ is called a locally repairable code (LRC) with locality $r$ if it can retrieve any coded symbol by at most $r$ other coded symbols. LRCs have been recently…
The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect…
Cyclic codes are an important class of linear codes. Bounding the minimum distance of cyclic codes is a long-standing research topic in coding theory, and several well-known and basic results have been developed on this topic. Recently,…
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
New asymptotic upper bounds are presented on the rate of sequences of locally repairable codes (LRCs) with a prescribed relative minimum distance and locality over a finite field $F$. The bounds apply to LRCs in which the recovery functions…
We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed sources in the finite block-length regime. Based on the convex optimization framework of the rate-distortion theory, we…
A $q$-ary $(n,k,r)$ locally repairable code (LRC) is an $[n,k,d]$ linear code over $\mathbb{F}_q$ such that every code symbol can be recovered by accessing at most $r$ other code symbols. The well-known Singleton-like bound says that $d \le…
In this work the construction of LRC codes given in [6] is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length $n \approx q^4$, dimension and…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
Recent work by Divsalar et al. has shown that properly designed protograph-based low-density parity-check (LDPC) codes typically have minimum (Hamming) distance linearly increasing with block length. This fact rests on ensemble arguments…
The maximum-likelihood decoding problem is known to be NP-hard for general linear and Reed-Solomon codes. In this paper, we introduce the notion of A-covered codes, that is, codes that can be decoded through a polynomial time algorithm A…
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…