Linear complementary pairs (LCP) of codes play an important role in armoring implementations against side-channel attacks and fault injection attacks. One of the most common ways to construct LCP of codes is to use Euclidean linear complementary dual (LCD) codes. In this paper, we first introduce the concept of linear codes with σ complementary dual (σ-LCD), which includes known Euclidean LCD c...

This article is motivated by the following local-to-global question: is every variety with tame quotient singularities globally the quotient of a smooth variety by a finite group? We show that this question has a positive answer for all quasi-projective varieties which are expressible as a quotient of a smooth variety by a split torus (e.g. simplicial toric varieties). Although simplicial toric...

D epartement de math ematiques Universit e du Qu ebec a Montr eal 0 PRELIMINARIES 1 Abstract One important challenge in non{parametric density and regression{function estimation is spatially inhomogeneous smoothness. This is often modelled by Besov-and Triebel{type smoothness constraints. Donoho and Johnstone (1992), Delyon and Juditsky (1993) studied minimax rates of convergence for wavelet es...

Given a family of Abelian varieties over a positive-dimensional base, we prove that for a sufficiently general curve in the base, every rational section of the family over the curve is contained in a unique rational section over the entire base. 1. Main results sec-intro The starting point for this article is the following theorem. Theorem 1.1. [GHMS05, Theorem 6.2] Let B be a smooth, quasi-pro...

We present Monte Carlo simulations on a new class of lattice models in which the degrees of freedom are elements of an Abelian or non-Abelian finite symmetry group G, placed on directed edges of a two-dimensional lattice. The plaquette group product is constrained to be the group identity. In contrast to discrete gauge models (but similar to past work on height models), only elements of symmetr...

Tarski associative groupoid (TA-groupoid) is a kind of non-associative satisfying law. In this paper, the new notions transposition regular TA-groupoid are proposed and their properties structural characteristics studied by using band quasi-separativity. particular, following conclusions strictly proved: (1) every left semigroup; (2) disjoint union sub Abelian groups; (3) finite with quasi-sepa...

Let G be a group and let k > 2 be an integer, such that (A: — 3)(A: — 1) < |G|/15 if G is finite. Suppose that the condition \A\ < k(k+l)/2 + (k-'i)/2 is satisfied by every it-element subset A c G. Then G is abelian. The proof uses the structure of quasi-invariant sets.

We introduce the notion of abelian fuzzy subsets on a groupoid, and we observe a variety of consequences which follow. New notions include, among others, diagonal symmetric relations, several types of quasi orders, convex sets, and fuzzy centers, some of whose properties are also investigated.

We construct non-trivial quasi-quantum groups associated to any nite group G and any element of H 3 (G; U(1)). We analyze the set of representations of these algebras and show that we recover the data of particular 3-dimensional topological eld theories. We also give the R-matrix structure in non abelian RCFT orbifold models.