相关论文: Direct construction of code loops
The matrix completion problem provides a unifying lens through which many fundamental problems in coding theory can be viewed. In this paper, we investigate Locally Recoverable Codes (LRCs) with Maximal Recoverability (MR) and Maximum…
Codes considered as structures within unit schemes greatly extends the availability of linear block and convolutional codes and allows the construction of these codes to required length, rate, distance and type. Properties of a code emanate…
Maintainable and general software allows developers to build robust applications efficiently, yet achieving these qualities often requires refactoring specialized solutions into reusable components. This challenge becomes particularly…
Large Language Models (LLMs) have demonstrated great potential for assisting developers in their daily development. However, most research focuses on generating correct code, how to use LLMs to generate personalized code has seldom been…
We relate a $l$-loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original $l$-loop graph. Causality requires that the propagators of the trees have a modified…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies…
Open-domain code generation aims to generate code in a general-purpose programming language (such as Python) from natural language (NL) intents. Motivated by the intuition that developers usually retrieve resources on the web when writing…
While there has been a lot of research recently on robots in household environments, at the present time, most robots in existence can be found on shop floors, and most interactions between humans and robots happen there. ``Collaborative…
Given a finite group $G$ and an extension of finite chain rings $S|R$, one can consider the group rings $\mathscr{S} = S[G]$ and $\mathscr{R} = R[G]$. The group ring $\mathscr{S}$ can be viewed as an $R$-bimodule, and any of its…
The paper establishes an one-to-one correspondence between simple Moufang loops and Paige loops constructed over Galois extension over prime field in its algebraic closure. Using this connection it describes fully the family of…
We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable…
We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notions such as distance, list-decoding, list-recovery, and…
Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction D$'$, and Forney's code formula are classical…
MDS codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field $F_q$ is completely solved for $q$ is…
In classical coding theory, it is common to construct new codes via propagation rules. There are various propagation rules to construct classical block codes. However, propagation rules have not been extensively explored for constructions…
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n,k. Among these new codes there is an optimal ternary…
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology invariants naturally give rise to diagonal logical gates. We…
In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from…