Related papers: Binary Subspace Codes in Small Ambient Spaces
A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
In this paper, we study two issues in asynchronous communication systems. The first issue is the derivation of sum capacity bounds for finite dimensional asynchronous systems. In addition, asymptotic results for the sum capacity bounds are…
Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component…
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…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
We introduce two new classes of covering codes in graphs for every positive integer $r$. These new codes are called local $r$-identifying and local $r$-locating-dominating codes and they are derived from $r$-identifying and…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
In the past few years, the study of receptive field codes has been of large interest to mathematicians. Here we give a complete characterization of receptive field codes realizable by connected receptive fields and we give the minimal…
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…
In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field. In this paper, the metric used is the so-called…
We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
Minimal codewords have applications in decoding linear codes and in cryptography. We study the maximum number of minimal codewords in binary linear codes of a given length and dimension. Improved lower and upper bounds on the maximum number…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\bf A}_q(n,d,k)$ of a set of $k$-dimensional subspaces in $\mathbb{F}_q^n$ such that the subspace distance satisfies $\operatorname{d_S}(U,V) =…
Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were…
Subspace codes and particularly constant dimension codes have attracted much attention in recent years due to their applications in random network coding. As a particular subclass of subspace codes, cyclic subspace codes have additional…
Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…