Abstract. The class of systems of uniform recurrence equations (UREs) is closed under unimodular transformations. As a result, every systolic array described by a unimodular mapping can be specified by a system of space-time UREs, in which the time and space coordinates are made explicit. As non-unimodular mappings are frequently used in systolic designs, this paper presents a method that deriv...

By using Construction A modulo 4 the following remarkable unimodular lattices have been constructed: the Gosset lattice E8, the Leech lattice, the 23 Niemeier lattices in dimension 24, the two extremal even unimodular lattices in dimension 32 with an automorphism of order 31, all the extremal unimodular lattices and the odd Leech lattice. In this survey, we review basic facts of life in the Z4 ...

The purpose of this note is to announce results obtained in the analytic continuation of the (nondegenerate) "principal series" of representations of the nXn complex unimodular group. This study has as its starting point a similar one for the 2X2 real unimodular group previously carried out by us in [4]. We let G be the nXn complex unimodular group and C its diagonal subgroup consisting of elem...

A golden lattice is an even unimodular Z[ 1+ √ 5 2 ]-lattice of which the Hilbert theta series is an extremal Hilbert modular form. We construct golden lattices from extremal even unimodular lattices and obtain families of dense modular lattices.

This paper provides a solution to the open problem of automatic rewriting loop nests for non-unimodular transformations. We present an algorithm that rewrites a loop nest under any non-singular (unimod-ular or non-unimodular) transformation. The algorithm works nicely with unimodular transformations being treated as a special case. The rst step of the algorithm calculates the loop bounds using ...

This paper focuses on covariant point-shifts of point processes on topological groups, which map points of a point process to other points of the point process in a translation invariant way. Foliations and connected components generated by point-shifts are studied, and the cardinality classification of connected components, previously known on Euclidean space, is generalized to unimodular grou...

A Golay Complementary Sequence (CS) has a Peak-to-AveragePower-Ratio (PAPR) ≤ 2.0 for its one-dimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2 CS, (GDJ CS), originate from certain quadratic cosets of Reed-Muller (1,m). These can be generated using the RudinShapiro construction. This paper shows that GDJ CS have a PAPR ≤ 2.0 under ...