Related papers: MDS or NMDS self-dual codes from twisted generaliz…
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…
In this work, we provide four methods for constructing new maximum sum-rank distance (MSRD) codes. The first method, a variant of cartesian products, allows faster decoding than known MSRD codes of the same parameters. The other three…
This preprint is of a chapter to appear in {\it Combinatorics and finite fields: Difference sets, polynomials, pseudorandomness and applications. Radon Series on Computational and Applied Mathematics}, K.-U. Schmidt and A. Winterhof (eds.).…
Maximum distance separable (MDS) codes and near MDS (NMDS) codes are of particular interest in coding theory due to their optimal error-correcting capabilities and wide applications in communication, cryptography, and storage systems. A…
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to…
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes,…
In this article, we present a new class of codes known as row-column twisted Reed-Solomon codes (abbreviated as RCTRS), motivated by the works of \cite{beelen2017twisted} and \cite{liu2025column}. We explicitly provide conditions for such…
In the recent paper entitled "Explicit constructions of MDS self-dual codes" accepted in { IEEE Transactions on Information Theory}, doi: 10.1109/TIT.2019.2954877, the author has constructed families of MDS self-dual codes from genus zero…
Maximum Distance Separable (MDS) convolutional codes are cha- racterized through the property that the free distance meets the generalized Singleton bound. The existence of free MDS convolutional codes over Z p r was recently discovered in…
The GM-MDS theorem, conjectured by Dau-Song-Dong-Yuen and proved by Lovett and Yildiz-Hassibi, shows that the generator matrices of Reed-Solomon codes can attain every possible configuration of zeros for an MDS code. The recently emerging…
Gabidulin codes are the first general construction of linear codes that are maximum rank distant (MRD). They have found applications in linear network coding, for example, when the transmitter and receiver are oblivious to the inner…
This paper considers the problem of designing maximum distance separable (MDS) codes over small fields with constraints on the support of their generator matrices. For any given $m\times n$ binary matrix $M$, the GM-MDS conjecture, due to…
In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It…
We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length $n$ of all QMDS codes with local dimension $D$ and distance $d \geq 3$ is bounded by $n \leq D^2 + d - 2$. We obtain their weight…
In this paper, we introduce codes equipped with pomset block metric. A Singleton type bound for pomset block codes is obtained. Code achieving the Singleton bound, called a maximum distance separable code (for short, MDS…
Given any linear code $C$ over a finite field $GF(q)$ we show how $C$ can be described in a transparent and geometrical way by using the associated Bruen-Silverman code. Then, specializing to the case of MDS codes we use our new approach to…
Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$,…
In this paper, we provide conditions that hulls of generalized Reed-Solomon (GRS) codes are also GRS codes from algebraic geometry codes. If the conditions are not satisfied, we provide a method of linear algebra to find the bases of hulls…
Reed-Solomon codes and Gabidulin codes have maximum Hamming distance and maximum rank distance, respectively. A general construction using skew polynomials, called skew Reed-Solomon codes, has already been introduced in the literature. In…
Cyclic maximum distance separable (MDS for short) codes are a special subclass of linear codes and have received a lot of attention, as these codes have very important applications in many areas including quantum codes, designs and finite…