相关论文: On Universally Decodable Matrices for Space-Time C…
Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of $[2^m+1, 2u-1, 2^m-2u+3]$ MDS codes for $1 \leq u \leq 2^{m-1}$, which are cyclic, reversible and BCH…
The construction of Maximum Distance Profile (MDP) convolutional codes in general requires the use of very large finite fields. In contrast convolutional codes with optimal column distances maximize the column distances for a given…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
We consider the problem of constructing linear Maximum Distance Separable (MDS) error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of…
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced…
The classical family of Reed-Solomon codes consist of evaluations of polynomials over the finite field $\mathbb{F}_q$ of degree less than $k$, at $n$ distinct field elements. These are arguably the most widely used and studied codes, as…
Let $K/F$ and $K/L$ be two cyclic Galois field extensions and $D=(K/F,\sigma,c)$ a cyclic algebra. Given an invertible element $d\in D$, we present three families of unital nonassociative algebras over $L\cap F$ defined on the direct sum of…
Consider the following framework of universal decoding suggested in [MerhavUniversal]. Given a family of decoding metrics and random coding distribution (prior), a single, universal, decoder is optimal if for any possible channel the…
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…
Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.
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…
In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the…
Code-based Distributed Matrix Multiplication (DMM) has been extensively studied in distributed computing for efficiently performing large-scale matrix multiplication using coding theoretic techniques. The communication cost and recovery…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
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…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
In this paper, we produce some new classes of entanglement-assisted quantum MDS codes(EAQMDS codes for short) via generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many EAQMDS codes…
In this paper we propose a new design criterion and a new class of unitary signal constellations for differential space-time modulation for multiple-antenna systems over Rayleigh flat-fading channels with unknown fading coefficients.…
Maximum distance separable (MDS) array codes constitute an important class of error-correcting codes due to their optimal distance properties and their relevance in distributed storage systems. In this paper, we investigate the construction…