Related papers: Representations of code loops by binary codes
C-loops are loops satisfying $x(y(yz))=((xy)y)z$. They often behave analogously to Moufang loops and they are closely related to Steiner triple systems and combinatorics. We initiate the study of C-loops by proving: (i) Steiner loops are…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
We classify all three-dimensional connected topological loops such that the group topologically generated by their left translations is the four-dimensional connected Lie group $G$ which has trivial center and precisely two one-dimensional…
We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank…
Non-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
Line codes make it possible to mitigate interference, to prevent short pulses, and to generate streams of bipolar signals with no direct-current (DC) power content through balancing. They find application in magnetic recording (MR) devices,…
In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves the base $2$ expansion of the integers in their defining…
The hull of a linear code is defined as the intersection of the code and its dual. This concept was initially introduced to classify finite projective planes. The hull plays a crucial role in determining the complexity of algorithms used to…
We give a complete characterization of simple graphs whose adjacency matrices generate binary linear complementary dual (LCD) codes. In particular, we completely characterize a distance-regular graph which yields an LCD code in terms of the…
This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.
The loop-tree duality (LTD) has become a novelty alternative to bootstrap the numerical evaluation of multi-loop scattering amplitudes. It has indeed been found that Feynman integrands, after the application of LTD, display a representation…
A de Bruijn array code is a set of $r \times s$ binary doubly-periodic arrays such that each binary $n \times m$ matrix is contained exactly once as a window in one of the arrays. Such a set of arrays can be viewed as a two-dimensional…
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most…
Binary code analysis allows analyzing binary code without having access to the corresponding source code. A binary, after disassembly, is expressed in an assembly language. This inspires us to approach binary analysis by leveraging ideas…
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $\mathbb{F}_q$ having large minimum weights for $q \in \{2,3\}$. Using the characterization, we…
Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…
Multidimensional convolutional codes generalize (one dimensional) convolutional codes and they correspond under a natural duality to multidimensional systems widely studied in the systems literature.
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. The aim of LP decoding is to develop an algorithm which has error-correcting performance…