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Constacyclic codes over finite fields are of theoretical importance as they are closely related to a number of areas of mathematics such as algebra, algebraic geometry, graph theory, combinatorial designs and number theory. However, the…

This paper considers the construction of isodual quasi-cyclic codes. First we prove that two quasi-cyclic codes are permutation equivalent if and only if their constituent codes are equivalent. This gives conditions on the existence of…

We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two…

Pseudo-geometric designs are combinatorial designs which share the same parameters as a finite geometry design, but which are not isomorphic to that design. As far as we know, many pseudo-geometric designs have been constructed by the…

Distributing qubits across quantum processing units (QPUs) connected by shared entanglement enables scaling beyond monolithic architectures. Hyperbolic Floquet codes use only weight-2 measurements and are good candidates for distributed…

We introduce graphcodes, a novel multi-scale summary of the topological properties of a dataset that is based on the well-established theory of persistent homology. Graphcodes handle datasets that are filtered along two real-valued scale…

The discovery of novel topological states has served as a major branch in physics and material science. However, to date, most of the established topological states of matter have been employed in Euclidean systems, where the interplay…

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…

We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.

In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions…

Concrete semi-realistic string/M theory constructions often predict the existence of new physics at the TeV scale, which may be different in character from the bottom-up ideas that are motivated by specific problems of the standard model. I…

This paper is devoted to the study of tessellations of the hyperbolic plane, especially the ones associated to hyperbolic triangle groups $\Delta(l,m,n)$. We give a full description of the cone types of these graphs and show that their…

The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…

In this paper we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules.…

Topological subsystem color codes (TSCCs) are an important class of topological subsystem codes that allow for syndrome measurement with only 2-body measurements. It is expected that such low complexity measurements can help in fault…

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however,…

We propose a new method for constructing partially hyperbolic diffeomorphisms on closed manifolds. As a demonstration of the method we show that there are simply connected closed manifolds that support partially hyperbolic diffeomorphisms.

Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…

This paper shows NP-completeness for finding Hamiltonian cycles in induced subgraphs of the dual graphs of semi-regular tessilations. It also shows NP-hardness for a new, wide class of graphs called augmented square grids. This work follows…