Related papers: Non-linear Cyclic Codes that Attain the Gilbert-Va…
Analytic combinatorics in several variables refers to a suite of tools that provide sharp asymptotic estimates for certain combinatorial quantities. In this paper, we apply these tools to determine the Gilbert-Varshamov (GV) bound for the…
We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…
We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.
The size of the Hamming distance spectrum of a code has received great attention in recent research. The main objective of this paper is to extend these significant theories to the $b$-symbol distance spectrum. We examine this question for…
We give an independent proof of the Krasikov-Litsyn bound d/n<~(1-5^{-1/4})/2 on doubly-even self-dual binary codes. The technique used (a refinement of the Mallows-Odlyzko-Sloane approach) extends easily to other families of self-dual…
We consider perturbed pendulum-like equations on the cylinder of the form $ \ddot x+\sin(x)= \varepsilon \sum_{s=0}^{m}{Q_{n,s} (x)\, \dot x^{s}}$ where $Q_{n,s}$ are trigonometric polynomials of degree $n$, and study the number of limit…
We study the asymptotic behavior of a family of algebraic geometry codes, which we call block-transitive, that generalizes the classes of transitive and quasi-transitive codes. We prove, by using towers of algebraic function fields, that…
The stationary Gross-Pitaevskii equation in one dimension is considered with a complex periodic potential satisfying the conditions of the PT (parity-time reversal) symmetry. Under rather general assumptions on the potentials we prove…
In this paper, we give an important isomorphism between contacyclic codes and cyclic codes over finite principal ideal rings. Necessary and sufficient conditions for the existence of non-trivial cyclic self-dual codes over finite principal…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…
Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of…
One formidable difficulty in quantum communication and computation is to protect information-carrying quantum states against undesired interactions with the environment. In past years, many good quantum error-correcting codes had been…
For a simple-root $\lambda$-constacyclic code $\mathcal{C}$ over $\mathbb{F}_q$, let $\langle\rho\rangle$ and $\langle\rho,M\rangle$ be the subgroups of the automorphism group of $\mathcal{C}$ generated by the cyclic shift $\rho$, and by…
We obtain a solution to a bordism version of Gromov's linearity problem over a large family of acyclic groups, for manifolds with arbitrary dimension. Every group embeds into some acyclic group in this family. Thus, the linear bordism…
In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over…
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic…
In this note, a class of error-correcting codes is associated to a toric variety associated to a fan defined over a finite field $\fff_q$, analogous to the class of Goppa codes associated to a curve. For such a ``toric code'' satisfying…
In this paper we prove that the Ball-Marsden-Slemrod controllability obstruction also holds for nonlinear equations, with integrable bilinear controls. We first show an abstract result and then we apply it to nonlinear wave equations. The…
Let $\mathbb{F}_p$ denote the finite field of order $p$, where $p$ is an odd prime. We study certain quantum negacyclic codes over $\mathbb{F}_p$ which we call $t$-Frobenius negacyclic codes. We obtain a criterion for constructing such…