相关论文: Strongly MDS Convolutional 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…
Maximum distance separable (MDS) codes are optimal error-correcting codes in the sense that they provide the maximum failure-tolerance for a given number of parity nodes. Suppose that an MDS code with $k$ information nodes and $r=n-k$…
Generalized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size. The study of codes…
The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes…
Higher order MDS codes are an interesting generalization of MDS codes recently introduced by Brakensiek, Gopi and Makam (IEEE Trans. Inf. Theory 2022). In later works, they were shown to be intimately connected to optimally list-decodable…
Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error…
In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The…
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…
An $[n,k,d]$ linear code is said to be maximum distance separable (MDS) or almost maximum distance separable (AMDS) if $d=n-k+1$ or $d=n-k$, respectively. If a code and its dual code are both AMDS, then the code is said to be near maximum…
The hull of a linear code is defined to be the intersection of the code and its dual. When the size of the hull is small, it has been proved that some algorithms for checking permutation equivalence of two linear codes and computing the…
We define the bidirectional distance profile (BDP) of a convolutional code as the minimum of the distance profiles of the code and its corresponding "reverse" code. We present tables of codes with the optimum BDP (OBDP), which minimize the…
In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order-$\ell$ MDS code, denoted by $\operatorname{MDS}(\ell)$, has the property that any $\ell$ subspaces formed from…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
A locally repairable code is called Singleton-optimal if it achieves the Singleton-type bound. Such codes are of great theoretic interest in the study of locally repairable codes. In the recent years there has been a great amount of work on…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
For high-rate maximum distance separable (MDS) codes, most of them are designed to optimally repair a single failed node by connecting all the surviving nodes. However, in practical systems, sometimes not all the surviving nodes are…
We construct a family of (n,k) convolutional codes with degree \delta in {k,n-k} that have a maximum distance profile. The field size required for our construction is of the order n^{2\delta}, which improves upon the known constructions of…
This paper studies the decoding capabilities of maximum distance profile (MDP) convolutional codes over the erasure channel and compares them with the decoding capabilities of MDS block codes over the same channel. The erasure channel…
An important family of quantum codes is the quantum maximum-distance-separable (MDS) codes. In this paper, we construct some new classes of quantum MDS codes by generalized Reed-Solomon (GRS) codes and Hermitian construction. In addition,…
The article provides a survey on convolutional codes stressing the connections to module theory and systems theory. Constructions of codes with maximal possible distance and distance profile are provided. The article will appear as book…