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Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg \cite{TB14} first gave a…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…
Cyclic codes are an important subclass of linear codes with wide applications in communication systems and data storage systems. In 2013, Ding and Helleseth presented nine open problems on optimal ternary cyclic codes $\mathcal{C}_{(1,e)}$.…
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the same length, is investigated. Lower and…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…
Three--dimensional colored triangulations are gluings of tetrahedra whose faces carry the colors 0, 1, 2, 3 and in which the attaching maps between tetrahedra are defined using the colors. This framework makes it possible to generalize the…
In this paper, we propose two new systematic ways to construct amicable orthogonal designs (AOD), with an aim to facilitate the construction of power-balanced orthogonal spacetime block codes (O-STBC) with favorable practical attributes. We…
The purpose of this paper is to study the cyclic self orthogonal codes over $\mathbb{Z}_{p^m}$. After providing the generator polynomial of cyclic self orthogonal codes over $\mathbb{Z}_{p^m}$, we give the necessary and sufficient condition…
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a…
This is the second in a series of papers in which we investigate ideal triangulations of the interiors of compact 3-manifolds with tori or Klein bottle boundaries. Such triangulations have been used with great effect, following the…
We study correlation functions of a conserved spin-1 current $J_\mu$ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point…
In this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring $R=\mathbb{F}_2+v\mathbb{F}_2+v^2\mathbb{F}_2$, where $v^3=1.$ These codes are defined as trace codes. They have the algebraic…
We study the conformal bootstrap constraints for 3D conformal field theories with a $\mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $\epsilon$ that is invariant under the symmetry. When there is additionally a…
Locally repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with $(r,\delta)$-locality that achieve the equality in the Singleton-type…
This research focuses on trajectory planning problems for autonomous vehicles utilizing numerical optimal control techniques. The study reformulates the constrained optimization problem into a nonlinear programming problem, incorporating…
Colored triangulations offer a generalization of combinatorial maps to higher dimensions. Just like maps are gluings of polygons, colored triangulations are built as gluings of special, higher-dimensional building blocks, such as octahedra,…