Related papers: New Constructions of MDS Symbol-Pair Codes
Let $C$ be a $(n,q^{2k},n-k+1)_{q^2}$ additive MDS code which is linear over ${\mathbb F}_q$. We prove that if $n \geqslant q+k$ and $k+1$ of the projections of $C$ are linear over ${\mathbb F}_{q^2}$ then $C$ is linear over ${\mathbb…
Recently, subfield codes of geometric codes over large finite fields $\gf(q)$ with dimension $3$ and $4$ were studied and distance-optimal subfield codes over $\gf(p)$ were obtained, where $q=p^m$. The key idea for obtaining very good…
Constructions of quantum MDS codes have been studied by many authors. We refer to the table in page 1482 of [3] for known constructions. However there are only few $q$-ary quantum MDS $[[n,n-2d+2,d]]_q$ codes with minimum distances…
MDS codes are elegant constructions in coding theory and have mode important applications in cryptography, network coding, distributed data storage, communication systems et. In this study, a method is given which MDS codes are lifted to a…
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting so-called \emph{Main Problem of Subspace Coding} is to determine the maximum size…
In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$,…
In this paper, a linear $\ell$-intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear $\ell$-intersection pair if their intersection has dimension…
We characterize Product-MDS pairs of linear codes, i.e.\ pairs of codes $C,D$ whose product under coordinatewise multiplication has maximum possible minimum distance as a function of the code length and the dimensions $\dim C, \dim D$. We…
Maximum distance separable convolutional codes are characterized by the property that the free distance reaches the generalized Singleton bound, which makes them optimal for error correction. However, the existing constructions of such…
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…
An $(n,k)$ maximum distance separable (MDS) code has optimal repair access if the minimum number of symbols accessed from $d$ surviving nodes is achieved, where $k+1\le d\le n-1$. Existing results show that the sub-packetization $\alpha$ of…
We propose three private information retrieval (PIR) protocols for distributed storage systems (DSSs) where data is stored using an arbitrary linear code. The first two protocols, named Protocol 1 and Protocol 2, achieve privacy for the…
Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum…
We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS…
A linear code is called an MDS self-dual code if it is both an MDS code and a self-dual code with respect to the Euclidean inner product. The parameters of such codes are completely determined by the code length. In this paper, we consider…
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,…
Let $\mathbb{F}_q$ be the finite field of $q$ elements, where $q=p^{m}$ with $p$ being a prime number and $m$ being a positive integer. Let $\mathcal{C}_{(q, n, \delta, h)}$ be a class of BCH codes of length $n$ and designed $\delta$. A…
A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$ generates a code of free distance at most ${\cal D} = D+2$ and, at best, a column distance profile (CDP) of $[2,3,\ldots,{\cal D}]$. A code is \emph{Maximum…
Self-dual maximum distance separable codes (self-dual MDS codes) and self-dual near MDS codes are very important in coding theory and practice. Thus, it is interesting to construct self-dual MDS or self-dual near MDS codes. In this paper,…
We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let $C$ be an $\mathbb F_q$-linear $(n,q^{hk},n-k+1)_{q^h}$ MDS code over $\mathbb F_{q^h}$. If $k=3$, $h \in…