Let R be a finite commutative chain ring with unique maximal ideal 〈γ〉, and let n be a positive integer coprime with the characteristic of R/〈γ〉. In this paper, the algebraic structure of cyclic codes of length n over R is investigated. Some new necessary and sufficient conditions for the existence of nontrivial self-dual cyclic codes are provided. An enumeration formula for the self-dual cycli...

In this note, we use a natural desingularization of the conormal variety of the variety of (n × n)-symmetric matrices of rank at most r to find a general formula for the algebraic degree in semidefinite programming. 1. The algebraic degree in semidefinite programming Let P be a general projective space of symmetric (n×n)−matrices up to scalar multiples, and let Yr ⊂ P m be the subvariety of mat...

Recently, the author has constructed families of MDS Euclidean self-dual codes from genus zero algebraic geometry (AG) codes. In present correspondence, more optimal AG are explored. New odd characteristic and those almost explicitly one curves, respectively. More curves higher genus.

The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding based on the solutions certain associated polynomial equations. proposed also makes it possible to identify conditions existence sought schemes.

1.2. Let E be a Euclidean vector space, Φ ⊂ E∗ a root system. Denote Q ⊂ h∗ the root lattice, and P ⊂ h∗ the weight lattice. Let Q∨ ⊂ E be the lattice generated by the coroots α∨, α ∈ Φ, the coroot lattice is dual to the weight lattice P ⊂ h∗, and P∨ ⊂ E the dual weight lattice, which is dual to the root lattice Q. Let H = HomZ(P,C) = Q∨ ⊗Z C∗ be the complex algebraic torus with Lie algebra h =...

This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we use this characterization to realize any constructible dual algebraic lattice as a possible initial segment of the degrees of constructibility. In a s...

In the study of algebraic groups the representative functions related to monoid algebras over fields provide an important tool which also yields the finite dual coalgebra of any algebra over a field. The purpose of this note is to transfer this basic construction to monoid algebras over commutative rings R. As an application we obtain a bialgebra (Hopf algebra) structure on the finite dual of t...

We prove that the boundary dynamics of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to have a finite Schreier graph in the boundary of the enriched dual pointed on some essentially...

We extend the target map, together with the weighted barriers and the notions of weighted analytic centers, from linear programming to general convex conic programming. This extension is obtained from a novel geometrical perspective of the weighted barriers, that views a weighted barrier as a weighted sum of barriers for a strictly decreasing sequence of faces. Using the Euclidean Jordan-algebr...

In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and C∗-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a quantisation of the Lie-Poisson structure of the dual of a Lie algebroid which deals with a big enough class of functions to include the above mentioned example. As an ...