4,245 research outputs found
Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
The concept of group divisible codes, a generalization of group divisible
designs with constant block size, is introduced in this paper. This new class
of codes is shown to be useful in recursive constructions for constant-weight
and constant-composition codes. Large classes of group divisible codes are
constructed which enabled the determination of the sizes of optimal
constant-composition codes of weight three (and specified distance), leaving
only four cases undetermined. Previously, the sizes of constant-composition
codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table
List Decodability at Small Radii
, the smallest for which every binary error-correcting code
of length and minimum distance is decodable with a list of size
up to radius , is determined for all . As a result,
is determined for all , except for 42 values of .Comment: to appear in Designs, Codes, and Cryptography (accepted October 2010
Violating Bell Inequalities Maximally for Two -Dimensional Systems
We investigate the maximal violation of Bell inequalities for two
-dimensional systems by using the method of Bell operator. The maximal
violation corresponds to the maximal eigenvalue of the Bell operator matrix.
The eigenvectors corresponding to these eigenvalues are described by asymmetric
entangled states. We estimate the maximum value of the eigenvalue for large
dimension. A family of elegant entangled states that violate
Bell inequality more strongly than the maximally entangled state but are
somewhat close to these eigenvectors is presented. These approximate states can
potentially be useful for quantum cryptography as well as many other important
fields of quantum information.Comment: 6 pages, 1 figure. Revised versio
Berry phase and quantum criticality in Yang--Baxter systems
Spin interaction Hamiltonians are obtained from the unitary Yang--Baxter
-matrix. Based on which, we study Berry phase and quantum
criticality in the Yang--Baxter systems.Comment: 7 pages, no figures. Accepted for publication in Annals of Physic
- …