This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes;they can ...
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This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes;they can be used in a variety of applications, including copyright protection for digital media, content authentication, media forensics, data binding, and covert communications. Some of these applications imply the presence of an adversary attempting to disrupt the transmission of information to the receiver;other applications involve a noisy, generally unknown, communication channel. Our focus is on the mathematical models, fundamental principles, and code design. techniques that are applicable to data hiding. The approach draws from basic concepts in information theory, coding theory, game theory, and signal processing, and is illustrated with applications to the problem of hiding data in images.
In this note we remark on certain “universal fixed messages” for the Rivest-Shamir-Adleman cryptosystem [1], and we describe how in certain cases these universal fixed messages can play a role in an attempt to break...
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In this note we remark on certain “universal fixed messages” for the Rivest-Shamir-Adleman cryptosystem [1], and we describe how in certain cases these universal fixed messages can play a role in an attempt to break the cryptosystem. This use of the universal fixed messages in an attempt to break the RSA cryptosystem† involves a certain prime factorization technique using the fixed messages. We characterize the situation in which such an attempt would be successful in practice, and we show that a user of the RSA cryptosystem can easily arrange to avoid this situation. Hence the use of the present technique does not pose a threat to the security of the RSA cryptosystem.
Chen and Cheng (Ann. Statist. 27 (1999) 1948) got the relationships between a blocked symmetrical factorial design and its residual design. In this paper, we extend the study to the case of blocked mixed-level factori...
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Chen and Cheng (Ann. Statist. 27 (1999) 1948) got the relationships between a blocked symmetrical factorial design and its residual design. In this paper, we extend the study to the case of blocked mixed-level factorial designs. By introducing a concept of blocked consulting design and using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain combinatorial identities that govern the relationships between the partitioned wordlength patterns of a blocked regular mixed factorial design and that of its blocked consulting design. Based on these identities, we furthermore establish some general rules for identifying minimum aberration blocked mixed factorial designs in terms of their blocked consulting designs. As applications, some blocked 4(1)2" and 4(2)2" designs with 16 and 32 runs are tabulated. (C) 2003 Elsevier B.V. All rights reserved.
Integer zeros of binary Krawtchouk polynomials occur in various problems of classical combinatorics. We present some of these properties and generalise them to q-Krawtchouk polynomials. We also give a survey of what i...
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Integer zeros of binary Krawtchouk polynomials occur in various problems of classical combinatorics. We present some of these properties and generalise them to q-Krawtchouk polynomials. We also give a survey of what is known about these zeros. (C) 2001 Academic Press.
In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributi...
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In this expository paper we show how one can, in a uniform way, calculate the weight distributions of some well-known binary cyclic codes. The codes are related to certain families of curves, and the weight distributions are related to the distribution of the number of rational points on the curves.
Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across cl...
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Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients;similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point;while the clients access the aggregated matrix in order to complete their tasks. The network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.
Abstract. Bose-Chaudhuri-Hocquenghem and Justesen codes are used to pack equa spheres in n–dimensional Euclidean space with density Δ satisfyingfor all sufficiently large n of the form m 2m, where m is a power of 4....
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Abstract. Bose-Chaudhuri-Hocquenghem and Justesen codes are used to pack equa spheres in n–dimensional Euclidean space with density Δ satisfyingfor all sufficiently large n of the form m 2m, where m is a power of 4. These appear to be the densest packings yet constructed in high dimensional space.
The research of developing efficient methodologies for constructing optimal experimental designs has been very active in the last decade. Uniform design is one of the most popular approaches, carried out by filling up...
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The research of developing efficient methodologies for constructing optimal experimental designs has been very active in the last decade. Uniform design is one of the most popular approaches, carried out by filling up experimental points in a determinately uniform fashion. Applications of coding theory in experimental design are interesting and promising. Quaternary codes and their binary Gray map images attracted much attention from those researching design of experiments in recent years. The present paper aims at exploring new results for constructing uniform designs based on quaternary codes and their binary Gray map images. This paper studies the optimality of quaternary designs and their two and three binary Gray map image designs in terms of the uniformity criteria measured by: the Lee, wrap-around, symmetric, centered and mixture discrepancies. Strong relationships between quaternary designs and their two and three binary Gray map image designs are obtained, which can be used for efficiently constructing two-level designs from four-level designs and vice versa. The significance of this work is evaluated by comparing our results to the existing literature.
When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Lab...
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When Jack van Lint was appointed as full professor at the Eindhoven University of Technology at the age of 26 he combined a PhD in number theory with a very open scientific mind. It took a sabbatical visit to Bell Laboratories in 1966 to make him understand that a new and fascinating field of applied mathematics was emerging: discrete mathematics. It fascinated and inspired him for the rest of his life. When he passed away on September 28, 2004, he left behind a legacy of 18 books and 177 articles, covering many aspects of coding theory, combinatorics, and finite geometry. van Lint was also a strong international advocate of the role that discrete mathematics ought to play in modern applied mathematics curricula. Quite a few departments sought his advice. Years later, four different universities showed their appreciation by awarding him an honorary degree. This overview is an homage to van Lint's academic achievements and can serve as an introduction to his work for younger generations. (c) 2006 Elsevier Inc. All rights reserved.
作者：
Ai, MYZhang, RCPeking Univ
Sch Math Sci LMAM Beijing 100871 Peoples R China Nankai Univ
Sch Math Sci Tianjin 300071 Peoples R China LPMC
Tianjin 300071 Peoples R China
In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain combinatorial identities that relate the wordlength pattern of a re...
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In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain combinatorial identities that relate the wordlength pattern of a regular mixed factorial design to that of its consulting design. According to these identities, we furthermore establish the general and unified rules for identifying minimum aberration mixed factorial designs through their consulting designs. It is an improvement and generalization of the results in Mukerjee and Wu (2001).
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