Related papers: A Construction of MDS Quantum Convolutional Codes
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…
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs…
Both maximum distance separable (MDS) codes that are not equivalent to generalized Reed-Solomon (GRS) codes (non-GRS MDS codes) and near MDS (NMDS) codes have nice applications in communication and storage systems. In this paper, we…
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS…
In this paper, we present an infinite family of MDS codes over $\mathbb{F}_{2^s}$ and two infinite families of almost MDS codes over $\mathbb{F}_{p^s}$ for any prime $p$, by investigating the parameters of the dual codes of two families of…
Let q be a power of 2. We show by representation theory that there exists a q x q unitary matrix of multiplicative order q+1 whose powers generate q+1 pairwise mutually unbiased base in C^q. When q is a power of an odd prime, there is a q x…
Multiple Input Double Output (MIDO) asymmetric space-time codes for 4 transmit antennas and 2 receive antennas can be employed in the downlink from base stations to portable devices. Previous MIDO code constructions with low Maximum…
In this article, we investigate properties of cyclic codes over a finite non-chain ring $\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$ where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid…
The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\mathbb{F}_q$, let $\operatorname{MEC}(k,q)$ denote the…
I report two general methods to construct quantum convolutional codes for quantum registers with internal $N$ states. Using one of these methods, I construct a quantum convolutional code of rate 1/4 which is able to correct one general…
We present a new propagation rule for CSS codes. Starting with a CSS code $[\![n,k,d]\!]_q$, we construct a CSS code with parameters $[\![n-2,k,d-1]\!]_q$. In general, one would only obtain a code with parameters $[\![n-2,k,d-2]\!]_q$. The…
A family of $\omega$-circulant balanced weighing matrices with classical parameters is used for the construction of optimal constant weight codes over an alphabet of size $g+1$ and length $n=(q^m -1)/(q-1)$, where $q$ is an odd prime power,…
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and improved estimates on the smallest field sizes over which such…
We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of…
In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the…
In this paper, the sufficient and necessary condition for the minimum distance of the BCH codes over $\mathbb{F}_q$ with length $q+1$ and designed distance 3 to be 3 and 4 are provided. Let $d$ be the minimum distance of the BCH code…
We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this…
Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…
A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length…
Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented.…