Non-full-rank Steiner quadruple systems S(v, 4, 3)

All different Steiner systems S(2 ^m , 4, 3) of order 2 ^m and rank 2 ^m ? m ? 1 + s over \(\mathbb{F}_2\) , where 0 ≤ s ≤ m ? 1, are constructed. The number of different systems S(2 ^m , 4, 3) whose incident matrices are orthogonal to a fixed code is obtained. A connection between the number of different Steiner systems and of different Latin cubes is described.     

On weak isometries of Preparata codes

Two codes C ₁ and C ₂ are said to be weakly isometric if there exists a mapping J: C ₁ → C ₂ such that for all x, y in C ₁ the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d, where d is the code distance of C ₁. We prove that Preparata codes of length n ≥ 2¹² are weakly isometric if and only if the codes are equivalent. A similar result is proved for punctured Preparata codes of length at least 2¹⁰ ? 1.     

Classification of Steiner quadruple systems of order 16 and rank at most 13<Superscript>1</Superscript>

A Steiner quadruple system SQS(v) of order v is a 3-design T (v, 4, 3, ) with = 1. In this paper we describe all nonisomorphic systems SQS(16) that can be obtained by the generalized concatenated construction (GC-construction). These Steiner systems have rank at most 13 over ₂. In particular, there is one system SQS(16) of rank 11 (points and planes of the a fine geometry AG(4, 2)), fifteen systems of rank 12, and 4131 systems of rank 13. All these Steiner systems are resolvable.Translated from Problemy Peredachi Informatsii, No. 4, 2004, pp. 48–67.Original Russian Text Copyright © 2004 by V. Zinoviev, D. Zinoviev.     

Generalized error-locating codes with component codes over the same alphabet

We consider generalized error locating (GEL) codes over the same alphabet for both component codes. We propose an algorithm for computing an upper bound on the decoding error probability under known input symbol error rate and code parameters. Is is used to construct an algorithm for selecting code parameters to maximize the code rate for a given construction and given input and output error probabilities. A lower bound on the decoding error probability is given. Examples of plots of decoding error probability versus input symbol error rate are given, and their behavior is explained.     

Watermark design based on Steiner triple systems

Constructing a set of watermarks of a specific structure may be one requirement for robust watermarking. This study aims to use the structure of Steiner triple systems to generate new watermarks. That is, the new watermark is a Steiner triple system built by using two smaller ones. The structure properties are examined to recognize watermarks at the receiver site. The main advantage is no information other than the mathematical structure has to be known for watermark recognition.Theoretical proof is given to verify the proposed watermark design method, and the experiment is conducted to confirm the theoretical behavior of the generated watermarks under random noise.     

Conflict-avoiding codes and cyclic triple systems

The paper deals with the problem of constructing a code of the maximum possible cardinality consisting of binary vectors of length n and Hamming weight 3 and having the following property: any 3 × n matrix whose rows are cyclic shifts of three different code vectors contains a 3 × 3 permutation matrix as a submatrix. This property (in the special case w = 3) characterizes conflict-avoiding codes of length n for w active users, introduced in [1]. Using such codes in channels with asynchronous multiple access allows each of w active users to transmit a data packet successfully in one of w attempts during n time slots without collisions with other active users. An upper bound on the maximum cardinality of a conflict-avoiding code of length n with w = 3 is proved, and constructions of optimal codes achieving this bound are given. In particular, there are found conflict-avoiding codes for w = 3 which have much more vectors than codes of the same length obtained from cyclic Steiner triple systems by choosing a representative in each cyclic class.     

Tilings of nonorientable surfaces by Steiner triple systems

A Steiner triple system of order n (for short, STS(n)) is a system of three-element blocks (triples) of elements of an n-set such that each unordered pair of elements occurs in precisely one triple. Assign to each triple (i,j,k) ? STS(n) a topological triangle with vertices i, j, and k. Gluing together like sides of the triangles that correspond to a pair of disjoint STS(n) of a special form yields a black-and-white tiling of some closed surface. For each n ≡ 3 (mod 6) we prove that there exist nonisomorphic tilings of nonorientable surfaces by pairs of Steiner triple systems of order n. We also show that for half of the values n ≡ 1 (mod 6) there are nonisomorphic tilings of nonorientable closed surfaces.     

Generalized L systems

This paper proposes the concept of generalized L systems, GL systems for short, which can describe asynchronized concurrent phenomena. We have proved that the GL systems are proper extensions of the traditional L systems. We have also defined a classification of GL systems and proved a sufficient and necessary condition for the equivalence of two subclasses of GL systems: two GPDOL (a class of deterministic GL systems) systems L[ m1, m2, ??? mj] and L[ n1, n2, ??? nk] are e-quivalent, iff k = j and there exists a common divisor g of all mi and a common divisor h of all nj such that (?) i: mi/g = nj/h.     

Generalized L systems

This paper proposes the concept of generalized L systems, GL systems for short, which can describe asynchronized concurrent phenomena. We have proved that the GL systems are proper extensions of the traditional L systems. We have also defined a classification of GL systems and proved a sufficient and necessary condition for the equivalence of two subclasses of GL systems: two GPD0L (a class of deterministic GL systems) systems L[m ₁, m ₂, …, m _j ] and L[n ₁, n ₂, …, n _k ] are equivalent, iff k = j and there exists a common divisor g of all m _l and a common divisor h of all n _l such that ? i: m _i/g = n _i/h.     

Generalized H2 control of discrete-time semi-Markov jump systems

This paper mainly studies the generalized H₂ control of discrete-time semi-Markov jump systems with bounded sojourn-time. By constructing the mode-dependent Lyapunov function related to the elapsed-time and the semi-Markov process, we obtain sufficient conditions to ensure the σ-error mean square stable and generalized H₂ performance of the semi-Markov jump system. Moreover, by introducing slack variables, the generalized H₂ performance index is reduced and the feasible region is expanded. Finally, through numerical calculations, we confirm the effectiveness of the design methods.     

Classification of steiner quadruple systems of order 16 and rank 14

All 708 103 nonisomorphic Steiner systems S(16, 4, 3) of order 16 and rank 14 over F ₂ are enumerated. Among them there are exactly 1059 homogeneous systems. It is shown that all the 708 103 Steiner systems can be obtained by the general doubling construction presented in the paper.     

Multi-GPU codes for spin systems simulations

We present and compare different approaches for using multiple Graphics Processing Units in the simulation of spin systems. As a benchmark we consider the time required to update a single spin of the 3D Heisenberg spin glass model, by using both the Over-relaxation and the Heat Bath algorithms. The results show that a suitable combination of techniques allows to hide almost completely the communication overhead by using the CPU as a communication co-processor of the GPU. Large scale simulations on clusters of GPUs can be efficiently carried out by following the same approach also for other applications where a clear cut exists between bulk and boundaries data.     

Generalized control systems,boundary control systems,and delayed control systems

We investigate the relationships between the three classes of systems mentioned in the title: we show that systems with delays in control are a special instance of boundary control systems, and a boundary control system produces a generalized control system when projected onto its (unstable) eigenspaces. We use this observation to investigate the action of feedback on the dynamical behavior of systems with boundary controls. In particular, the well-known fact that spectral controllability is necessary and sufficient for a system with delays in control to be stabilizable is derived from a general rather than from anad hoc method. This paper was written according to the programs of the GNAFA-CNR group, with the financial support of the Italian “Ministero della Pubblica Istruzione.”     

多输入多输出通信系统的低密度奇偶校验码

受低解码复杂度下空时编码的全分集大编码增益的启发,提出了基于多输入多输出通信系统的低密度奇偶校验码的高效率设计。该设计可以在接收端很好地解决内迭代和外迭代的权衡,以增强解码的性能和灵活性。仿真结果表明,给出的编码在多输入多输出信道上性能良好。     

Hierarchical codes: A flexible trade-off for erasure codes in peer-to-peer storage systems

Redundancy is the basic technique to provide reliability in storage systems consisting of multiple components. A redundancy scheme defines how the redundant data are produced and maintained. The simplest redundancy scheme is replication, which however suffers from storage inefficiency. Another approach is erasure coding, which provides the same level of reliability as replication using a significantly smaller amount of storage. When redundant data are lost, they need to be replaced. While replacing replicated data consists in a simple copy, it becomes a complex operation with erasure codes: new data are produced performing a coding over some other available data. The amount of data to be read and coded is d times larger than the amount of data produced, where d, called repair degree, is larger than 1 and depends on the structure of the code. This implies that coding has a larger computational and I/O cost, which, for distributed storage systems, translates into increased network traffic. Participants of Peer-to-Peer systems often have ample storage and CPU power, but their network bandwidth may be limited. For these reasons existing coding techniques are not suitable for P2P storage. This work explores the design space between replication and the existing erasure codes. We propose and evaluate a new class of erasure codes, called Hierarchical Codes, which allows to reduce the network traffic due to maintenance without losing the benefits given by traditional erasure codes.     

Z_(p~2)上的循环码和负循环码

应用了Gray映射φ的概念,给出了Zpk+1中的1-pk-循环码与Fp上指标为pk-1长度为pkn的准循环码之间的关系;同时定义了Zp2→Zp2n的映射φ,并且研究了在它作用下负循环码与循环码的关系。     

Generalized Besicovitch and Weyl spaces: Topology, patterns, and sliding block codes

The Besicovitch and Weyl topologies on the space of configurations take a point of view completely different from the usual product topology; as such, the properties of the former are much different from that of the latter. The one-dimensional case has already been the subject of thorough studies; we extend it to greater dimensions, and also to more general groups.