Steganography is the hiding of secret information within innocent-looking information (e.g., text, audio, image, video, etc.). A quantum version of steganography is a method based on quantum physics. In this paper, we...
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Steganography is the hiding of secret information within innocent-looking information (e.g., text, audio, image, video, etc.). A quantum version of steganography is a method based on quantum physics. In this paper, we propose quantum steganography by combining quantum error-correcting codes with prior entanglement. In many steganographic techniques, embedding secret messages in error-correcting codes may cause damage to them if the embedded part is corrupted. However, our proposed steganography can separately create secret messages and the content of cover messages. The intrinsic form of the cover message does not have to be modified for embedding secret messages. (C) 2015 Elsevier B.V. All rights reserved.
A coordinate of a binary code of size M is said to be balanced if the number of zero and ones in the coordinate is either or (that is, exactly for even M). Since good codes (of various types) tend to be balanced in al...
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A coordinate of a binary code of size M is said to be balanced if the number of zero and ones in the coordinate is either or (that is, exactly for even M). Since good codes (of various types) tend to be balanced in all coordinates, various conjectures have been made regarding the existence of such codes. It is here shown that there are parameters for which there are no optimal binary error-correcting codes with a balanced coordinate. This is proved by the code attaining , which is shown to be unique here;denotes the maximum size of a binary code of length n and minimum distance d. It is further shown that .
作者：
Yoshida, BeniMIT
Ctr Theoret Phys Cambridge MA 02139 USA CALTECH
Inst Quantum Informat & Matter Pasadena CA 91125 USA
Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper boun...
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Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations. (C) 2013 Elsevier Inc. All rights reserved.
作者：
Mihara, TakashiToyo Univ
Dept Informat Sci & Arts 2100 Kujirai Kawagoe Saitama 3508585 Japan
Steganography has been proposed as a data hiding technique. As a derivation, quantum steganography based on quantum physics has also been proposed. In this paper, we extend the results in presented (Mihara, Phys. Lett...
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Steganography has been proposed as a data hiding technique. As a derivation, quantum steganography based on quantum physics has also been proposed. In this paper, we extend the results in presented (Mihara, Phys. Lett. 379, 952 2015) and propose a multiparty quantum steganography technique that combines quantum error-correcting codes with entanglement. The proposed protocol shares an entangled state among n + 1 parties and sends n secret messages, corresponding to the n parties, to the other party. With no knowledge of the other secret messages, the n parties can construct a stego message by cooperating with each other. Finally, we propose a protocol for sending qubits using the same technique.
Cellular Automata (CA) are a promising architecture for computers with nanometer-scale sized components, because their regular structure potentially allows chemical manufacturing techniques based on self-organization....
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Cellular Automata (CA) are a promising architecture for computers with nanometer-scale sized components, because their regular structure potentially allows chemical manufacturing techniques based on self-organization. With the increase in integration density, however, comes a decrease in the reliability of the components from which such computers will be built. This paper employs BCH error-correcting codes to construct CA with improved reliability. We construct an asynchronous CA of which a quarter of the (ternary) bits storing a cell's state information may be corrupted without affecting the CA's operations, provided errors are evenly distributed over a cell's bits (no burst errors allowed). Under the same condition, the corruption of half of a cell's bits can be detected.
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In partic...
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We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise asymptotic estimates on the density functions of several classes of codes that are extremal with respect to minimum distance, covering radius, and maximality. The techniques developed in this paper apply to various distance functions, including the Hamming and the rank metric distances. Applications of our results show that, unlike the F-qm-linear MRD codes, the F-q-linear MRD codes are not dense in the family of codes of the same dimension. More precisely, we show that the density of F-q-linear MRD codes in F-q(nxm) in the set of all matrix codes of the same dimension is asymptotically at most 1/2, both as q -> +infinity and as m -> +infinity. We also prove that MDS and F-qm-linear MRD codes are dense in the family of maximal codes. Although there does not exist a direct analogue of the redundancy bound for the covering radius of Fq-linear rank metric codes, we show that a similar bound is satisfied by a uniformly random matrix code with high probability. In particular, we prove that codes meeting this bound are dense. Finally, we compute the average weight distribution of linear codes in the rank metric, and other parameters that generalize the total weight of a linear code. (C) 2019 Published by Elsevier Inc.
The multicovering radii of a code are natural generalizations of the covering radius in which the goal is to cover all m-tuples of vectors for some m as cheaply as possible. In this correspondence, we describe several...
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The multicovering radii of a code are natural generalizations of the covering radius in which the goal is to cover all m-tuples of vectors for some m as cheaply as possible. In this correspondence, we describe several techniques for obtaining lower bounds on the sizes of codes achieving a given multicovering radius. Our main method is a generalization of the method of linear inequalities based on refined weight distributions of the code. We also obtain a linear upper bound on the 2-covering radius. We further study bounds on the sizes of codes with a given multicovering radius that are subcodes of a fixed code. We rind, for example, constraints on parity checks for codes with small ordinary covering radius.
Molecular dynamics (MD) simulations rely on the accurate evaluation and integration of Newton's equations of motion to propagate the positions of atoms in proteins during a simulation. As such, one can expect them...
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Molecular dynamics (MD) simulations rely on the accurate evaluation and integration of Newton's equations of motion to propagate the positions of atoms in proteins during a simulation. As such, one can expect them to be sensitive to any form of numerical error that may occur during a simulation. Increasingly graphics processing units (GPUs) are being used to accelerate MD simulations. Current GPU architectures designed for high performance computing applications support error-correcting codes (ECC) that detect and correct single bit-flip soft error events in GPU memory;however, this error checking carries a penalty in terms of simulation speed. ECC is also a major distinguishing feature between high performance computing NVIDIA Tesla cards and the considerably more cost-effective NVIDIA GeForce gaming cards. An argument often put forward for not using GeForce cards is that the results are unreliable because of the lack of ECC. In an initial attempt to quantify these concerns, an investigation of the reproducibility of GPU-accelerated MD simulations using the AMBER software was conducted on the XSEDE supercomputer Keeneland, a cluster at Los Alamos National Laboratory, and a cluster at the San Diego Supercomputer Center. While the data collected are insufficient to make solid conclusions and more extensive testing is needed to provide quantitative statistics, the absence of ECC events and lack of any silent errors in all the simulations conducted to date suggest that these errors are exceedingly rare and as such the time and memory penalty of ECC may outweigh the utility of error checking functionality. However, a considerable amount of error originating from defective hardware was observed, which suggests that rigorous acceptance testing should be performed on new GPU-based systems by repeatedly running reproducible yet realistic calculations.
A fast method to compute the minimum Lee weight and the symmetrized weight enumerator of extended quadratic residue codes (XQR-codes) over the ring Z(4) is developed. Our approach is based on the classical Brouwer-Zim...
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A fast method to compute the minimum Lee weight and the symmetrized weight enumerator of extended quadratic residue codes (XQR-codes) over the ring Z(4) is developed. Our approach is based on the classical Brouwer-Zimmermann algorithm and additionally takes advantage of the large group of automorphisms and the self-duality of the Z(4)-linear XQR-codes as well as the projection to the binary XQR-codes. As a result, the hitherto unknown minimum Lee distances of all Z(4)-linear XQR-codes of lengths between 72 and 104 and the minimum Euclidean distances for the lengths 72, 80, and 104 are computed. It turns out that the binary Gray image of the Z(4)-linear XQR-codes of lengths 80 and 104 has higher minimum distance than any known linear binary code of equal length and cardinality. Furthermore, the Z(4)-linear XQR-code of length 80 is a new example of an extremal Z(4)-linear type II code. Additionally, we give the symmetrized weight enumerator of the Z(4)-linear XQR-codes of lengths 72 and 80, and we correct the weight enumerators of the Z(4)-linear XQR-code of length 48 given by Pless and Qian and Bonnecaze et al.
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