Related papers: Two new classes of quantum MDS codes
This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the…
Twisted generalized Reed-Solomon (TGRS) codes, as a flexible extension of classical generalized Reed-Solomon (GRS) codes, have attracted significant attention in recent years. In this paper, we construct two classes of LCD codes from the…
Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we…
In this paper, we present a new family of maximum rank distance (MRD for short) codes in $\mathbb F_{q}^{2n\times 2n}$ of minimum distance $2\leq d\leq 2n$. In particular, when $d=2n$, we can show that the corresponding semifield is exactly…
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…
We investigate additive codes, defined as $\mathbb{F}_q$-linear subspaces $C \subseteq \mathbb{F}_{q^h}^n$ of length $n$ and dimension $r$ over $\mathbb{F}_q$. An additive code is said to be of type $[n, r/h, d]_q^h$, where $d$ denotes the…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
We study (symbol-pair) codes for symbol-pair read channels introduced recently by Cassuto and Blaum (2010). A Singleton-type bound on symbol-pair codes is established and infinite families of optimal symbol-pair codes are constructed. These…
We construct six new explicit families of linear maximum sum-rank distance (MSRD) codes, each of which has the smallest field sizes among all known MSRD codes for some parameter regime. Using them and a previous result of the author, we…
Linearized Reed-Solomon (LRS) codes are evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary…
Let $p$ be an odd prime and $r,s,m$ be positive integers. In this study, we initiate our exploration by delving into the intricate structure of all repeated-root cyclic codes and their duals with a length of $2^rp^s$ over the finite field…
A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have…
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…
Reed-Solomon (RS) codes are among the most ubiquitous codes due to their good parameters as well as efficient encoding and decoding procedures. However, RS codes suffer from having a fixed length. In many applications where the length is…
Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…
In their seminal 1989 work (IEEE Trans. Inf. Theory 35(3):655-657), Roth and Lempel constructed a well-known family of non-Reed-Solomon maximum distance separable (MDS) codes. For decades, this family of codes has attracted extensive…
Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new…
Since near maximum distance separable (NMDS) codes have good algebraic properties and excellent error-correcting capabilities, they have been widely used in various fields such as communication systems, data storage, quantum codes, and so…
Let $M_{q}(k)$ be the maximum length of MDS codes with parameters $q,k$. In this paper, the properties of $M_{q}(k)$ are studied, and some new upper bounds of $M_{q}(k)$ are obtained. Especially we obtain that $M_{q}(q-1)\leq…
Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…