Related papers: On mutually $\mu$-intersecting quasi-Hermitian var…

In this paper, we develop some foundations for a theory of algebraic varieties of congruences on commutative semirings. By studying the structure of congruences, firstly, we show that the spectrum $ \text{Spec}^{c}(A) $ consisting of prime…

An Orthogonally resolvable Matching Design OMD$(n, k)$ is a partition of the edges the complete graph $K_n$ into matchings of size $k$, called blocks, such that the blocks can be resolved in two different ways. Such a design can be…

Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal curves. Along this side of research, we provide new examples of…

In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian G-space. Our argument closely follows the methods of a 1998 paper of…

Given a weighted flag variety $w\Sigma(\mu,u)$ corresponding to chosen fixed parameters $\mu$ and $u$, we present an algorithm to compute lists of all possible projectively Gorenstein $n$-folds, having canonical weight $k$ and isolated…

Let $(Q,\mathfrak{n})$ be a regular local ring of dimension $c \geq 2$ with algebraically closed residue field $k = Q/\mathfrak{n}$. Let $f_1, f_2, \ldots f_{c-1}, g$ be a regular sequence in $Q$ such that $ f_i \in \mathfrak{n}^2$ for all…

In this paper, we construct some new classes of complete permutation monomials with exponent $d=\frac{q^n-1}{q-1}$ using AGW criterion (a special case). This proves two recent conjectures in [Wuetal2] and extends some of these recent…

We show how to obtain linear combinations of polynomials in an orthogonal sequence $\{P_n\}_{n\geq 0}$, such as $Q_{n,k}(x)=\sum\limits_{i=0}^k a_{n,i}P_{n-i}(x)$, $a_{n,0}a_{n,k}\neq0$, that characterize quasi-orthogonal polynomials of…

We propose a framework to give a precise meaning to the intuitive notion of "family of real forms of a variety parametrised by a variety" and study some fundamental properties of this notion. As an illustration, for any $n \geq 1$, we…

Let $E/F$ be a quadratic extension of non-archimedean local fields of characteristic 0 and let $G=U(n)$, $H=U(m)$ be unitary groups of hermitian spaces $V$ and $W$. Assume that $V$ contains $W$ and that the orthogonal complement of $W$ is a…

It has been a great challenge to construct new quantum MDS codes. In particular, it is very hard to construct quantum MDS codes with relatively large minimum distance. So far, except for some sparse lengths, all known $q$-ary quantum MDS…

Let $q$ be a prime power. Let $\lambda>1$ be a divisor of $q-1$, and let $\tau>1$ and $\rho>1$ be divisors of $q+1$. Under certain conditions we prove that there exists an MDS stabilizer quantum code with length $n=\lambda \tau \sigma$…

We prove that the recently shown cohomological obstruction for quasiregular ellipticity has a generalization in the theory of quasiregular values. More specifically, if $M$ is a closed, connected, and oriented Riemannian $n$-manifold, and…

The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a "quasi-fermion"…

Near maximum distance separable (NMDS) codes, where both the code and its dual are almost maximum distance separable, play pivotal roles in combinatorial design theory and cryptographic applications. Despite progress in fixed dimensions…

Given a (2N - 1)-dimensional projective space over GF(2), PG(2N - 1, 2), and its geometric spread of lines, there exists a remarkable mapping of this space onto PG(N - 1, 4) where the lines of the spread correspond to the points and…

Consider the moment map $\mu \colon T^*(\mathfrak{p} \times \mathbb{C}^n) \to \mathfrak{p}^*$ for a parabolic subalgebra $\mathfrak{p}$ of $\mathfrak{gl}_n(\mathbb{C})$. We prove that the preimage of $0$ under $\mu$ is a complete…

In this paper,we show some $[2n,2n-2,3]$ and $[2n,2n-3,4]$ MDS codes over dihedral codes $F_qD_{2n}$,in the case $n$ is odd and char$F_q$$\nmid$$\lvert G \rvert$ and $F_q$ contains primitive root of exponent $\lvert G \rvert$ i.e $F_q$ is…

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of…

The paper studies the interpolation properties of net spaces $N_{p,q}(M)$, when $M$ is the set of dyadic cubes in $\mathbb{R}^n$, and also when $M$ is the family of all cubes with parallel faces to the coordinate axes in $\mathbb{R}^n$. It…