Related papers: A Singleton Bound for Lattice Schemes
We introduce the concepts of complex Grassmannian codes and designs. Let G(m,n) denote the set of m-dimensional subspaces of C^n: then a code is a finite subset of G(m,n) in which few distances occur, while a design is a finite subset of…
Non-overlapping codes have been studied for almost 60 years. In such a code, no proper, non-empty prefix of any codeword is a suffix of any codeword. In this paper, we study codes in which overlaps of certain specified sizes are forbidden.…
An improved Singleton-type upper bound is presented for the list decoding radius of linear codes, in terms of the code parameters [n,k,d] and the list size L. L-MDS codes are then defined as codes that attain this bound (under a slightly…
Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum…
The Johnson-type upper bound on the maximum size of a code of length $n$, distance $d=2w-1$ and constant composition ${\overline{w}}$ is $\lfloor\dfrac{n}{w_1}\rfloor$, where $w$ is the total weight and $w_1$ is the largest component of…
In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an…
We investigate universal bounds on spherical codes and spherical designs that could be obtained using Delsarte's linear programming methods. We give a lower estimate for the LP upper bound on codes, and an upper estimate for the LP lower…
Subsystem codes are a generalization of noiseless subsystems, decoherence free subspaces, and quantum error-correcting codes. We prove a Singleton bound for GF(q)-linear subsystem codes. It follows that no subsystem code over a prime field…
The list-decodable code has been an active topic in theoretical computer science.There are general results about the list-decodability to the Johnson radius and the list-decoding capacity theorem. In this paper we show that rates,…
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Reed-Solomon codes (Hamming metric) and Gabidulin codes (rank…
Reed--Solomon codes are a well--studied code class which fulfill the Singleton bound with equality. However, their length is limited to the size $q$ of the underlying field $\mathbb{F}_q$. In this paper we present a code construction which…
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…
This paper considers $n= 128$ dimensional construction A lattice design, using binary codes with known minimum Hamming distance and codeword multiplicity, the number of minimum weight codeword. A truncated theta series of the lattice is…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor $\log\log n$ for infinitely many dimensions $n$. Here we prove an effective version of this result, in the sense that we exhibit, for the same…
A locally repairable code is called Singleton-optimal if it achieves the Singleton-type bound. Such codes are of great theoretic interest in the study of locally repairable codes. In the recent years there has been a great amount of work on…
A Lattice is a partially ordered set where both least upper bound and greatest lower bound of any pair of elements are unique and exist within the set. K\"{o}tter and Kschischang proved that codes in the linear lattice can be used for error…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
In this work, we propose a family of single-node second-order boundary schemes for the lattice Boltzmann method with general collision terms. The construction of the schemes is quite universal and simple, it does not involve concrete…