相关论文: Galois Self-Dual Constacyclic Codes
Galois images of polycyclic codes over a finite chain ring $S$ and their annihilator dual are investigated. The case when a polycyclic codes is Galois-disjoint over the ring $S,$ is characterized and, the trace codes and restrictions of…
The Lambek-Grishin calculus is a symmetric extension of the Lambek calculus: in addition to the residuated family of product, left and right division operations of Lambek's original calculus, one also considers a family of coproduct, right…
We develop a Galois (descent) theory for comonads within the framework of bicategories. We give generalizations of Beck's theorem and the Joyal-Tierney theorem. Many examples are provided, including classical descent theory, Hopf-Galois…
Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes…
This article examines group ring codes over finite fields and finite groups. We also present a section on two-dimensional cyclic codes in the quotient ring $\mathbb{F}_q[x, y] / \langle x^{l} - 1, y^{m} - 1 \rangle$. These two-dimensional…
Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes,…
We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a…
By using our previous results on induced Hopf Galois structures and a recent result by Koch, Kohl, Truman and Underwood on normality, we determine which types of Hopf Galois structures occur on Galois extensions with Galois group isomorphic…
We study isomonodromicity of systems of parameterized linear differential equations and related conjugacy properties of linear differential algebraic groups by means of differential categories. We prove that isomonodromicity is equivalent…
This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…
In this paper, we present some necessary and sufficient conditions under which an irreducible polynomial is self-reciprocal (SR) or self-conjugate-reciprocal (SCR). By these characterizations, we obtain some enumeration formulas of SR and…
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse…
This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial…
It is well-known that all Feynman integrals within a given family can be expressed as a finite linear combination of master integrals. The master integrals naturally group into sectors. Starting from two loops, there can exist sectors made…
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…
In this paper, we establish Galois theory for partial differential systems defined over formally real differential fields with a real closed field of constants and over formally $p$-adic differential fields with a $p$-adically closed field…
It is shown that the Galois closure of the henselization of a one dimensional local field arising in geometric and arithmetic situation is separably closed.
We determine conditions for the invariance of the gonality under base extension, depending on the numeric invariants of the curve. More generally, we study the Galois descent of morphisms of curves to Brauer-Severi varieties, and also of…
Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum…
In \cite{anote}, Wu and Shi studied $ l $-Galois LCD codes over finite chain ring $\mathcal{R}=\mathbb{F}_q+u\mathbb{F}_q$, where $u^2=0$ and $ q=p^e$ for some prime $p$ and positive integer $e$. In this work, we extend the results to the…