Leo Storme

Bio: Leo Storme is an academic researcher from Ghent University. The author has contributed to research in topics: Blocking set & Prime (order theory). The author has an hindex of 24, co-authored 195 publications receiving 2612 citations. Previous affiliations of Leo Storme include National Fund for Scientific Research.

The packing problem in statistics, coding theory and finite projective spaces : update 2001

Abstract: This article updates the authors’ 1998 survey [134] on the same theme that was written for the Bose Memorial Conference (Colorado, June 7–11, 1995). That article contained the principal results on the packing problem, up to 1995. Since then, considerable progress has been made on different kinds of subconfigurations.

Galois geometries and coding theory

Abstract: Galois geometries and coding theory are two research areas which have been interacting with each other for many decades. From the early examples linking linear MDS codes with arcs in finite projective spaces, linear codes meeting the Griesmer bound with minihypers, covering radius with saturating sets, links have evolved to functional codes, generalized projective Reed---Muller codes, and even further to LDPC codes, random network codes, and distributed storage. This article reviews briefly the known links, and then focuses on new links and new directions. We present new results and open problems to stimulate the research on Galois geometries, coding theory, and on their continuously developing and increasing interactions.

Generating the group of reversible logic gates

Abstract: Reversible logic plays a fundamental role both in ultra-low power electronics and in quantum computing. It is therefore important to have an insight into the structure of the group formed by the reversible logic gates and their cascading into reversible circuits. Such insight is gained from constructing chains of maximal subgroups. The subgroup of control gates plays a prominent role, as it is a Sylow 2-subgroup.

Synthesis of reversible logic circuits

Abstract: Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics, and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT, and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting the distribution of circuit sizes. We also study canonical circuit decompositions where gates of the same kind are grouped together. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.

Constructions and Properties of k out of nVisual Secret Sharing Schemes

Abstract: The idea of visual k out of n secret sharing schemes was introduced in Naor. Explicit constructions for k = 2 and k = n can be found there. For general k out of n schemes bounds have been described. Here, two general k out of n constructions are presented. Their parameters are related to those of maximum size arcs or MDS codes. Further, results on the structure of k out of n schemes, such as bounds on their parameters, are obtained. Finally, the notion of coloured visual secret sharing schemes is introduced and a general construction is given.

Algebraic Geometric Codes: Basic Notions

Abstract: The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc The authors give a unique perspective on the subject Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory There are no prerequisites other than a standard algebra graduate course The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively Special attention is given to the geometry of curves over finite fields in the third chapter Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes

Synthesis and optimization of reversible circuits—a survey

Abstract: Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, postsynthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms—search based, cycle based, transformation based, and BDD based—as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.