In a previous work [4] we found a relation between the ranks of codiagonal matrices (matrices with 0's in their diagonal and non-zeroes elsewhere) and the quality of explicit Ramsey-graph constructions. We also gave there a construction based on the BBR-polynomial of Barrington, Beigel and Rudich [1]. In the present work we give another construction for low-rank co-diagonal matrices, based on a...

We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for the tensor product theory are constrained if the allowed modular invariants of the individual conformal field theory factors have been classified. We illustrat...

We investigate properties of two-weight codes over finite Frobenius rings, giving constructions for the modular case. A δ-modular code [15] is characterized as having a generator matrix where each column g appears with multiplicity δ|gR×| for some δ ∈ Q. Generalizing [10] and [5], we show that the additive group of a two-weight code satisfying certain constraint equations (and in particular a m...

The arithmetic of quaternions is recalled from a constructive point of view. A Hecke module is introduced, defined as a free abelian group on right ideal classes of a quaternion order, together with a natural action of Hecke operators. An equivalent construction in terms of Shimura curves is then introduced, and the quaternion construction is applied to the analysis of specific modular and Shim...

We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The construction is divided into four steps and each step gives a mathematical structure of independent interest. These mathematical structures are intertwining operator algebras, genus-zero modular functors, ge...

The construction of reactive systems often requires the combination of different individual functionalities, thus leading to a complex overall behavior. To achieve an efficient construction of reliable systems, a structured approach to the definition of the behavior is needed. Here, functional modularization supports a separation of the overall functionality into individual functions as well as...

Languages that are used for Software Language Engineering (SLE) offer a range of features that support the construction and deployment of new languages. SLE languages offer features for constructing and processing syntax and defining the semantics of language features. New languages may be embedded within an existing language (internal) or may be stand-alone (external). Modularity is a desirabl...

Software transformation methods are enacted during a migration project to perform the technical transition of a legacy system to a new environment. A critical task of each project is to construct a situation-specific transformation method. In this paper, we categorize current Situational Method Engineering (SME) approaches that support the construction of situation-specific transformation metho...

This paper generalizes Elkies’ construction of error-correcting nonlinear codes found in [N. Elkies, Excellent nonlinear codes from modular curves, in: Proceedings of the 33rd Annual ACM Symposium on the Theory of Computing, STOC’01, Hersonissos, Crete, Greece, 2001, pp. 200–208]. The generalization produces a precise average code size over codes in the new construction. The result is a larger ...

This paper concerns the problem of building reactive systems in a modular way. Several institutions have been proposed for the specification of reactive systems throughout the last fifteen years. Based on the institutions, formalisms for the incremental construction of system specifications have been developed. Related problem of modular construction of system implementations has received less ...