Datta and Johnsen (Des. Codes Cryptogr., {\bf{91}} (2023), 747-761) introduced a new family of evalutation codes in an affine space dimension $\ge 2$ over finite field $\mathbb{F}_q$ where linear combinations elementary symmetric polynomials are evaluated on the set all points with pairwise distinct coordinates. In this paper, we propose generalization by taking low dimensional systems polynomials. Computation for small values $q=7,9$ shows that carefully chosen generalized Datta-Johnsen...

For a finite group G let Γ(G) denote the graph defined on non-identity elements of in such way that two distinct vertices are connected by an edge if and only they generate G. In this paper it is shown contains Hamiltonian cycle for many groups

Abstract A loop is (right) automorphic if all its inner mappings are automorphisms. Using the classification of primitive groups small degrees, we show that there no non-associative simple commutative order less than 2 12 , and 2500. We obtain numerous examples right loops. also prove every has antiautomorphic inverse property, a only conjugations

In this paper we give an infinite class of finite simple right Bol loops exponent 2. The multiplication group these is extension elementary Abelian $2$-group by $S_5$. construction uses the description structure such given M. Aschbacher (2005). These results answer some questions Aschbacher.

In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every Leibniz algebra g with dim[g,g]=1 is isotopic to Heisenberg Lie or l2n+1J1, where J1 n × Jordan block eigenvalue 1. also prove two such algebras are if and only racks integrating them isotopic. This gives classification whose tangent space at unit element a one-dimensional commutator ideal. Eventually, introduce new invariants for racks.

Hermitian functional and differential codes are AG-codes defined on a curve. To ensure good performance, the divisors defining such have to be carefully chosen, exploiting rich combinatorial algebraic properties of curves. In this paper, case C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ω</sub> (D, mT) curve ℋ xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> 3 over F 6 is worked out where su.yppp(T) := 3(F 2), set all 2-rational points 3,...

We study a new extension formula for right Bol loops. prove the necessary or sufficient conditions to be Bol. describe most important invariants: multiplication group, nuclei, and center. show that core is an involutory quandle which disjoint union of two isomorphic quandles. also derive further results on structure group extension.

We prove that every finite, commutative automorphic loop is solvable. also <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-loop The main idea of the proof to associate a simple Lie algebra characteristic </inline-formula> hypothetical finite loop. “crust thin sandwich” theorem...

In this paper we propose a framework for automated forecasting of energy-related time series using open access data from European Network Transmission System Operators Electricity (ENTSO-E). The provides forecasts various countries publicly available historical only. Our solution was benchmarked the actual load and country provided estimates (where available). We conclude that proposed system can produce timely with comparable prediction accuracy in number cases. also investigate...