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IEEE TRANSACTIONS ON INFORMATION THEORY 1997年第1期43卷 136-146页

作者： Jungnickel, D Vanstone, SA UNIV WATERLOO DEPT COMBINATOR & OPTIMIZAT WATERLOO ON N2L 3G1 CANADA

It is well-known that the set of all even subgraphs of a connected graph G on p vertices with q edges forms a binary linear code C = C-E(G) with parameters [q, q - p + 1, g], where g is the girth of G. Such codes were studied systematically by Bredeson and Hakimi [7], [14] who were concerned with the problems of augmenting C to a larger [q, k, g]-code and of efficiently decoding such augmented graphical codes, We will give a new approach to these problems by requiring the augmented codes to be graphical (i,e,, they should still consist of spanning subgraphs of G), On one hand, we present two construction methods which turn out to contain the methods proposed by Hakimi and Bredeson [14] as special cases (even though it is not clear from their paper that their augmented codes are in fact graphical), As we will show, this not only gives a better understanding of their construction, it also results in augmenting codes of larger dimension. We look at the case of 1-error-correcting graphical codes in some detail, In particular, we show how to obtain the extended Hamming codes as ''purely'' graphical codes by our approach, On the other hand, we follow a suggestion of Ntafos and Hakimi [26] and use techniques from combinatorial optimization to give decoding procedures for graphical codes which turn out to be considerably more efficient than the approach via majority logic decoding proposed by Bredeson and Hakimi. We also consider the decoding problem for the even graphical code based on the complete graph K-2n in more detail: we discuss an efficient hardware implementation of an encoding/decoding scheme for these codes and we also show that things may be arranged in such a way that one can also correct all adjacent double errors, Finally, we briefly discuss nonlinear graphical codes.

关键词： graphical code binary code decoding algorithm Chinese postman problem

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Construction of all tournament matrices with prescribed row sum vector

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DISCRETE APPLIED MATHEMATICS 2014年 171卷 147-152页

作者： Hacioglu, Ilhan Kurkcu, Burak Canakkale Onsekiz Mart Univ Arts & Sci Fac Dept Math TR-17100 Canakkale Turkey

In this article, we define the binary codes of tournament matrices in the class T(R) and give unique construction algorithms for matrices which have minimum and maximum binary codes. By introducing a generating algorithm with an order we show that all matrices in class T(R) can be sorted uniquely between matrices with minimum and maximum binary codes. (C) 2014 Elsevier B.V. All rights reserved.

关键词： binary code Tournament matrix Generating algorithm

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An optimization of a non-volatile latch using memristors for sequential circuit applications

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ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING 2022年第1期110卷 55-61页

作者： Rziga, Faten Ouaja Mbarek, Khaoula Ghedira, Sami Besbes, Kamel Univ Monastir Microelect & Instrumentat Lab Monastir Tunisia Sousse Technopole Ctr Res Microelect & Nanotechnol Sousse Tunisia

The next generation of non-volatile memory elements have been attracting significant attention for future emerging memory applications in recent years. Several technologies have been developed to occupy a new field in storage-class memory and even replace NAND flash memories in sequential logic applications, due to their advantageous features such as fast programming time, low power consumption, high endurance and retention. Latch topologies have been proposed to implement these new technologies. In this article, we present new non-volatile Latch topology. We focus on a D Latch topology that uses memristors as memory elements combined with CMOS components. The memristor device has been implemented using an accurate Verilog-A model exploring the experimental data of a real OxRRAM device. Our simulation results explore low-voltage and reliable non-volatile Latch designs. Indeed, we integrate this Latch design to behave as a counter application using both binary and Gray codes. Moreover, this topology has been compared with other non-volatile topologies in terms of power consumption, cell size, energy, programing time and robustness at different programming voltage values. We proved that the memristor-based Latch has non-volatile characteristics and is able to store data.

关键词： Memristor Non-volatile Verilog-A model Latch Flip-flop binary code Gray code

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binary construction of quantum codes of minimum distances five and six

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DISCRETE MATHEMATICS 2008年第9期308卷 1603-1611页

作者： Li, Ruihu Li, Xueliang Air Force Engn Univ Dept Appl Math & Phys Coll Sci Xian 710051 Shaanxi Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China Nankai Univ Ctr Combinator Tianjin 300071 Peoples R China

In this paper, we construct a large number of good quantum codes of minimum distances five and six by Steane's Construction. Our methods involve the study of the check matrices of binary extended BCH-codes, togeth... 详细信息

关键词： binary code self-orthogonal code quantum (error-correcting) code

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A note on binary grammatical codes of trees

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THEORETICAL COMPUTER SCIENCE 1996年第2期155卷 425-438页

作者： Ehrenfeucht, A tenPas, P Rozenberg, G UNIV COLORADO DEPT COMP SCIBOULDERCO 80309 LEIDEN UNIV DEPT COMP SCI2300 RA LEIDENNETHERLANDS

Grammatical codes of trees provide a way to encode ordered trees into strings over a finite alphabet in such a way that the length of each code-word is precisely the number of leaves of the coded tree. Such codes are grammatical because they result by applying production rules of a grammar G to a tree t which becomes then a derivation tree t' in G and the yeild of this derivation tree t' becomes the code-word for t. Grammatical codes were investigated in [2, 3], see also [1]. In this note we present two topics related to binary grammatical codes. The first topic (see Section 2) is grammatical codes of binary trees with a minimal code alphabet. It is shown that the only binary codes that are minimal in this sense are the so-called ''strict'' binary codes (as considered in [3]). The second topic (see Section 3) concerns the extension of binary grammatical codes to grammatical codes for trees of arbitrary degree. We make comparisons between classes of codes obtained in this way and the classes from [2, 3]. In Section 1 we recall (from [2, 3]) some notions and results concerning grammatical codes.

关键词： trees Road Trees codeword binary Classes binary code codes Two thirds binary trees Cosmic strings

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Statically-Directed Dynamic Taint Analysis

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Chinese Journal of Electronics 2014年第1期23卷 18-24页

作者： CHEN Kai ZHANG Yingjun State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences Trusted Computing and Information Assurance Laboratory Institute of Software Chinese Academy of Sciences

Taint analysis is a popular method in software analysis field including vulnerability/malware analysis. By identifying taint source and making suitable taint propagation rules, we could directly know whether variables in software have any relationship with input *** taint analysis method is efficient, but it is imprecise since runtime information is lacked. Dynamic taint analysis method usually instruments every instruction in software to catch the taint propagation process. However, this is inefficient since it usually takes lots of time for context switches between original code and instrumenting code. In this paper, we propose a statically-directed dynamic taint analysis method to increase the efficiency of taint analysis process without any loss of accuracy. In this way, there is no need to instrument every instruction. Several experiments are made on our prototype SDTaint and the results show that our method is several times more efficient than traditional dynamic taint analysis method.

关键词： Taint analysis Statically-directed Dynamic analysis binary code

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binary linear complementary dual codes

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2019年第4期11卷 677-696页

作者： Harada, Masaaki Saito, Ken Tohoku Univ Res Ctr Pure & Appl Math Grad Sch Informat Sci Sendai Miyagi 9808579 Japan

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual [n, k] codes with the largest minimum weight among all binary linear complementary dual [n, k] codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete classification of binary linear complementary dual [n, k] codes with the largest minimum weight is also given for 1 <= k <= n <= 16.

关键词： binary code Linear complementary dual code K-cover

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ON LINEAR STRUCTURE AND PHASE ROTATION INVARIANT PROPERTIES OF BLOCK M-PSK MODULATION codeS

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IEEE TRANSACTIONS ON INFORMATION THEORY 1991年第1期37卷 164-167页

作者： KASAMI, T TAKATA, T FUJIWARA, T SHU, L UNIV HAWAII MANOA DEPT ELECT ENGN HONOLULU HI 96822 USA

Two important structural properties of block M(=2/sup '/)-ary PSK modulation codes, linear structure and phase symmetry, are investigated. An M-ary modulation code is first represented as a code with symbols from the integer group S/sub M-PSK/=(0,1,2,---,M-1) under modulo-M addition. Then the linear structure of block M-PSK modulation codes over S/sub M-PSK/ with respect to modulo-M vector addition is defined, and conditions are derived under which a block M-PSK modulation code is linear. Once the linear structure is developed, the phase symmetry of block M-PSK modulation codes is studied. In particular, a necessary and sufficient condition for a block M-PSK modulation code that is linear as a binary code to be invariant under 2/sup h/180 degrees /M phase rotation, for 1>or=h>or=l is derived. Finally, a list of short 8-PSK and 16-PSK modulation codes is given, together with their linear structure and the smallest phase rotation for which a code is invariant.

关键词： Signs and symbols lineation phase symmetry multiple phase shift keying binary code codes Invariant phase rotation modulation coding

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EFFICIENT binary codeS FOR EXTREMELY HIGH-DIMENSIONAL DATA

EFFICIENT BINARY CODES FOR EXTREMELY HIGH-DIMENSIONAL DATA

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IEEE International Conference on Image Processing

作者： Tsung-Yu Lin Tyng-Luh Liu Inst. of Inf. Sci. Taipei Taiwan

ISBN: (纸本)9781479957521

Recent advances in tackling large-scale computer vision problems have supported the use of an extremely high-dimensional descriptor to encode the image data. Under such a setting, we focus on how to efficiently carry out similarity search via employing binary codes. Observe that most of the popular high-dimensional descriptors induce feature vectors that have an implicit 2-D structure. We exploit this property to reduce the computation cost and high complexity. Specifically, our method generalizes the Iterative Quantization (ITQ) framework to handle extremely high-dimensional data in two steps. First, we restrict the dimensionality-reduction projection to a block-diagonal form and decide it by independently solving several moderate-size PCA sub-problems. Second, we replace the full rotation in ITQ with a bilinear rotation to improve the efficiency both in training and testing. Our experimental results on a large-scale dataset and comparisons with a state-of-the-art technique are promising.

关键词： binary codes cryptography image coding iterative methods 2D structure bilinear rotation block-diagonal form dimensionality-reduction projection extremely high-dimensional data feature vectors high-dimensional descriptors iterative quantization framework binary codes Computer vision Pattern recognition Principal component analysis Quantization (signal) Training Vectors binary code hashing similarity search binary code hashing image coding images computer vision iterative methods cryptography Pattern recognition principal components analysis Functional training Eigenvector Improved Transmission Quality

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BCK-codes Based on a Parity Check Matrix

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FUNDAMENTA INFORMATICAE 2020年第2期174卷 137-165页

作者： Keshavarzian, Nazanin Saeid, Arsham Borumand Tehranian, Abolfazl Islamic Azad Univ IAU Dept Math Sci & Res Branch Tehran Iran Shahid Bahonar Univ Kerman Dept Pure Math Fac Math & Comp Kerman Iran

Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks.

关键词： BCI/BCK-algebra binary code linear code parity check matrix error-detecting Hamming distance incidence structure BCK-incidence vector Algorithm Orthogonal code Atom Generator matrix

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