相关论文: Algebraic Construction of Tail-Biting Trellises fo…
In this article, we present two new approaches to construct minimal linear codes of dimension $n+1$ over $\mathbb{F}_{3}$ using characteristic and ternary functions. We also obtain the weight distributions of these constructed minimal…
In this paper, we investigate the algebraic structure for polycyclic codes over a specific class of serial rings, defined as $\mathscr R=R[x_1,\ldots, x_s]/\langle t_1(x_1),\ldots, t_s(x_s) \rangle$, where $R$ is a chain ring and each…
Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties,…
We first review various known algebraic structures on the Hochschild (co)homology of a differential graded algebras under weak Poincar{\'e} duality hypothesis, such as Calabi-Yau algebras, derived Poincar{\'e} duality algebras and closed…
We construct a quantum Dolbeault double complex $\oplus_{p,q}\Omega^{p,q}$ on the quantum plane $\Bbb C_q^2$. This solves the long-standing problem that the standard differential calculus on the quantum plane is not a $*$-calculus, by…
We propose reducible algebraic curves as a mechanism to construct Partial MDS (PMDS) codes geometrically. We obtain new general existence results, new explicit constructions and improved estimates on the smallest field sizes over which such…
We describe a procedure, called regularisation, that allows us to study geometric structures on Lie algebroids via foliated geometric structures on a manifold of higher dimension. This procedure applies to various classes of Lie algebroids;…
Twilled L(ie)-R(inehart) algebas generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an almost twilled pre-LR algebra, which is a true twilled LR-algebra iff the almost…
In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese Remainder…
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…
We investigate Chevalley bases for extended affine Lie algebras of type $A_1$.The concept of integral structures for extended affine Lie algebras of rank greater than one has been successfully explored in recent years. However, for the rank…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
We propose a simple model of entanglement generated by geometry, studying non-relativistic massive L\'evy-Leblond fermions in the $1+2$ geometry of a Bronnikov-Ellis wormhole. The model is equivalent to that of relativistic massless Dirac…
In 1999 Chas and Sullivan discovered that the homology H_*(LX) of the space of free loops on a closed oriented smooth manifold X has a rich algebraic structure called string topology. They proved that H_*(LX) is naturally a…
A method for compiling quantum algorithms into specific braiding patterns for non-Abelian quasiparticles described by the so-called Fibonacci anyon model is developed. The method is based on the observation that a universal set of quantum…
In this paper we generalize correspondence theorems of Mikhalkin and Nishinou-Siebert providing a correspondence between algebraic and parameterized tropical curves. We also give a description of a canonical tropicalization procedure for…
We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of…
We present an affine $sl (n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax…