Списочное декодирование вейвлет-кодов

В работе обсуждается возможность списочного декодирования вейвлет-кодов и приводится утверждение, согласно которому вейвлет-коды над полем $GF(q)$ нечетной характеристики с длиной кодовых и информационных слов $n=q-1$ и $n/2$ соответственно, а также над полем четной характеристики с длиной кодовых и информационных слов $n=q-1$ и $(n-1)/2$ соответственно допускают списочное декодирование, если среди коэффициентов спектрального представления их порождающих многочленов имеется $d+1$ последовательных нулей, $0$ < $d$ < $n/2$ для полей нечетной характеристики и $0$ < $d$ < $(n-3)/2$ для полей четной характеристики. Также описывается алгоритм, позволяющий выполнять списочное декодирование вейвлет-кодов при соблюдении перечисленных условий. В качестве демонстрации его работы приводятся пошаговые решения модельных задач списочного декодирования зашумленных кодовых слов вейвлет-кодов над полями четной и нечетной характеристики. Помимо этого, в работе построена вейвлет-версия квазисовершенного троичного кода Голея, длины его кодовых и информационных слов равны 8 и 4 соответственно, кодовое расстояние равно 4, минимальный радиус шаров с центрами в кодовых словах, покрывающих пространство слов длины 8, равен 3

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

Constructions in public-key cryptography over matrix groups

ISBN : 978-0-8218-4037-5International audienceThe purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new homomorphic public-key cryptosystem. They rely on difficulty of the conjugacy and membership problems for subgroups of a given group. To support these and other known cryptographic schemes we present a general technique to produce a family of instances being matrix groups (over finite commutative rings) which play a role for these schemes similar to the groups $Z_n^*$ in the existing cryptographic constructions like RSA or discrete logarithm

Finite Fields: Theory and Applications

Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation

HPC-GAP: engineering a 21st-century high-performance computer algebra system

Symbolic computation has underpinned a number of key advances in Mathematics and Computer Science. Applications are typically large and potentially highly parallel, making them good candidates for parallel execution at a variety of scales from multi-core to high-performance computing systems. However, much existing work on parallel computing is based around numeric rather than symbolic computations. In particular, symbolic computing presents particular problems in terms of varying granularity and irregular task sizes thatdo not match conventional approaches to parallelisation. It also presents problems in terms of the structure of the algorithms and data. This paper describes a new implementation of the free open-source GAP computational algebra system that places parallelism at the heart of the design, dealing with the key scalability and cross-platform portability problems. We provide three system layers that deal with the three most important classes of hardware: individual shared memory multi-core nodes, mid-scale distributed clusters of (multi-core) nodes, and full-blown HPC systems, comprising large-scale tightly-connected networks of multi-core nodes. This requires us to develop new cross-layer programming abstractions in the form of new domain-specific skeletons that allow us to seamlessly target different hardware levels. Our results show that, using our approach, we can achieve good scalability and speedups for two realistic exemplars, on high-performance systems comprising up to 32,000 cores, as well as on ubiquitous multi-core systems and distributed clusters. The work reported here paves the way towards full scale exploitation of symbolic computation by high-performance computing systems, and we demonstrate the potential with two major case studies

Tuple Interpretations for Higher-Order Complexity

We develop a class of algebraic interpretations for many-sorted and higher-order term rewriting systems that takes type information into account. Specifically, base-type terms are mapped to tuples of natural numbers and higher-order terms to functions between those tuples. Tuples may carry information relevant to the type; for instance, a term of type nat may be associated to a pair ? cost, size ? representing its evaluation cost and size. This class of interpretations results in a more fine-grained notion of complexity than runtime or derivational complexity, which makes it particularly useful to obtain complexity bounds for higher-order rewriting systems. We show that rewriting systems compatible with tuple interpretations admit finite bounds on derivation height. Furthermore, we demonstrate how to mechanically construct tuple interpretations and how to orient ? and ? reductions within our technique. Finally, we relate our method to runtime complexity and prove that specific interpretation shapes imply certain runtime complexity bounds