相关论文: Improved Nearly-MDS Expander Codes
It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…
The singleton defect of an $[n,k,d]$ linear code ${\cal C}$ is defined as $s({\cal C})=n-k+1-d$. Codes with $S({\cal C})=0$ are called maximum distance separable (MDS) codes, and codes with $S(\cal C)=S(\cal C ^{\bot})=1$ are called near…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
Symbol-pair codes are proposed to combat pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. Maximum distance separable (MDS)…
The present paper mainly studies limits and constructions of insertion and deletion (insdel for short) codes. The paper can be divided into two parts. The first part focuses on various bounds, while the second part concentrates on…
The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended…
Insertion-deletion codes (insdel codes for short) play an important role in synchronization error correction. The higher the minimum insdel distance, the more insdel errors the code can correct. Haeupler and Shahrasbi established the…
Quantum error correction is fundamentally important for quantum information processing and computation. Quantum error correction codes have been studied and constructed since the pioneering papers of Shor and Steane. Optimal (called MDS)…
Locally repairable codes which are optimal with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known…
The notion of universally decodable matrices (UDMs) was recently introduced by Tavildar and Viswanath while studying slow fading channels. It turns out that the problem of constructing UDMs is tightly connected to the problem of…
Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial codes over finite fields, renowned for achieving list decoding capacity. These codes have found a wide range of applications beyond the traditional scope…
Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
Recently, it was discovered by several authors that a $q$-ary optimal locally recoverable code, i.e., a locally recoverable code archiving the Singleton-type bound, can have length much bigger than $q+1$. This is quite different from the…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes…
Locally recoverable codes are widely used in distributed and cloud storage systems. The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out…
In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of…
Systematic constructions of MDS self-dual codes is widely concerned. In this paper, we consider the constructions of MDS Euclidean self-dual codes from short length. Indeed, the exact constructions of MDS Euclidean self-dual codes from…
For linear codes, the MacWilliams Extension Theorem states that each linear isometry of a linear code extends to a linear isometry of the whole space. But, in general, it is not the situation for nonlinear codes. In this paper it is proved,…