相关论文: Asymptotically Good Quantum Codes
A new class of space time codes with high performance is presented. The code design utilizes tailor-made permutation codes, which are known to have large minimal distances as spherical codes. A geometric connection between spherical and…
Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a standalone method of computation of Gaussian…
In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…
Let $q$ be a prime power and let $\mathcal{R}=\mathbb{F}_{q}[u_1,u_2, \cdots, u_k]/\langle f_i(u_i),u_iu_j-u_ju_i\rangle$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq k$ are polynomials, not all linear, which split into…
Asymptotic formulas of the number of various partitions are studied, like 3-colored partitions, concave partitions, certain plane partitions, partitions without small parts, the number of p-rings.
A kind of self-dual quasi-abelian codes of index $2$ over any finite field $F$ is introduced. By counting the number of such codes and the number of the codes of this kind whose relative minimum weights are small, such codes are proved to…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
A quantum theory of asymptotically flat space-times is presented using the solutions of the Null Surface Formulation (NSF) field equations in a perturbative scheme. Free-field commutation relations are given for the null free data of NSF at…
We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Most known quantum codes are additive, meaning the codespace can be described as the simultaneous eigenspace of an abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood…
We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.
In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key…
This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
Graph codes play an important role in photonic quantum technologies as they provide significant protection against qubit loss, a dominant noise mechanism. Here, we develop methods to analyse and optimise measurement-based tolerance to qubit…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…