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2nd Sino-Foreign-Interchange Workshop on Intelligence Science and Intelligent Data Engineering (IScIDE)

作者： Zhang, Xuanping Liang, Zhigang Shao, Liping Zhang, Yuqian Chen, Qingyuan Shaanxi Normal Univ Sch Comp Sci Xian 710062 Peoples R China Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian 710049 Peoples R China Northwest Polytech Univ Sch Comp Sci Xian 710129 Peoples R China

ISBN: (纸本)9783642319181;9783642319198

In traditional chaotic map based image encryption algorithm, the encryption performance is determined by the permutation generating speed, and due to short periodical problem led by the finite precision effect, the permutation generating is always in a low efficient. In this paper, a method to generate a large permutation by combining several small permutation arrays is proposed by introducing a join operation to improve the permutation generating speed, where small permutation arrays are generated by one-dimensional chaotic map. Based on this permutation generating, an image encryption algorithm is proposed where XOR and MOD based diffusion procedures are added. The complete image encryption algorithm is a multiple rounds of substitution-permutation network where permutation and diffusion as the basic building blocks. Experiments show that the proposed algorithm is a key-sensitive, can resist different attacks such as differential attack and plaintext attack, and the ciphered image is similar to a noise image.

关键词： Chaotic permutation array Image encryption permutation

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permutation arrays for powerline communication and mutually orthogonal Latin squares

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IEEE TRANSACTIONS ON INFORMATION THEORY 2004年第6期50卷 1289-1291页

作者： Colbourn, CJ Klove, T Ling, ACH Arizona State Univ Dept Comp Sci & Engn Tempe AZ 85287 USA Univ Bergen Dept Informat N-5020 Bergen Norway Univ Vermont Dept Comp Sci Burlington VT 05405 USA

We develop a connection between permutation arrays that are used in powerline communication and well-studied combinatorial objects, mutually orthogonal latin squares (MOLS). From this connection, many new results on p... 详细信息

关键词： doubly resolvable design mutually orthogonal Latin squares (MOLS) permutation array permutation code powerline communications

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On the construction of permutation arrays via mappings from binary vectors to permutations

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DESIGNS CODES AND CRYPTOGRAPHY 2006年第2期40卷 139-155页

作者： Huang, Yen-Ying Tsai, Shi-Chun Wu, Hsin-Lung Natl Chiao Tung Univ Dept Comp Sci Hsinchu 30050 Taiwan

An (n, d, k)-mapping f is a mapping from binary vectors of length n to permutations of length n + k such that for all x, y is an element of {0, 1}(n), d(H) (f (x), f (y)) >= d(H)(x, y) + d, if d(H) (x, y) <= (n + k)-d and d(H) (f (x), f (y)) = n + k, if d(H) (x, y) > (n + k)-d. In this paper, we construct an (n, 3, 2)-mapping for any positive integer n >= 6. An (n, r)-permutation array is a permutation array of length n and any two permutations of which have Hamming distance at least r. Let P (n, r) denote the maximum size of an (n, r)-permutation array and A (n, r) denote the same setting for binary codes. Applying (n, 3, 2)-mappings to the design of permutation array, we can construct an efficient permutation array (easy to encode and decode) with better code rate than previous results [Chang (2005). IEEE Trans inf theory 51:359-365, Chang et al. (2003). IEEE Trans Inf Theory 49:1054-1059;Huang et al. (submitted)]. More precisely, we obtain that, for n >= 8, P(n, r) >= A(n-2, r-3) > A(n-1, r-2) = A (n, r-1) when n is even and P(n, r) >= A(n-2, r-3) = A(n-1, r-2) > A(n, r-1) when n is odd. This improves the best bound A(n-1, r-2) so far [Huang et al. (submitted)] for n >= 8.

关键词： permutation array coding theory

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A New Construction of permutation arrays

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2012年第11期E95A卷 1855-1861页

作者： Park, Jung Youl Song, Hong-Yeop Attached Inst ETRI Taejon South Korea Yonsei Univ Sch Elect & Elect Engn Dept Elect & Elect Engn Seoul 120749 South Korea

Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA (pm, p(m-1) k) for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has (vertical bar PA(p, k) . p((m-1)(p-k)))(m) rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k >= 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA (p(m), p(m-1) k) for a given index i very simply.

关键词： permutation array error correcting code

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Decoding permutation arrays with ternary vectors

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DESIGNS CODES AND CRYPTOGRAPHY 2011年第1期61卷 1-9页

作者： Lee, Chia-Jung Lin, Te-Tsung Shieh, Min-Zheng Tsai, Shi-Chun Wu, Hsin-Lung Natl Chiao Tung Univ Dept Comp Sci Hsinchu Taiwan

We give an explicit decoding scheme for the permutation arrays under Hamming distance metric, where the encoding is constructed via a distance-preserving mapping from ternary vectors to permutations (3-DPM).

关键词： permutation array Ternary code Decoding Hamming distance

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A decomposition of Fl(n)^d indexed by permutation arrays

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ADVANCES IN APPLIED MATHEMATICS 2000年第2期25卷 212-227页

作者： Eriksson, K Linusson, S Malardalens Hogskola Dept Math & Phys SE-72123 Vasteras Sweden Stockholm Univ Dept Math SE-10691 Stockholm Sweden

We study a decomposition of Fl(n)(d-1), where: Fl(n) denotes the flag manifold over C-n. The strata are defined by the dimensions of intersections of one space from each fag, so for d equal to 2 this is the usual Bruhat cell decomposition, The strata are indexed by "permutation arrays," which are d-dimensional analogs of permutation matrices. We present a partial order on these permutation arrays, specializing: to the Bruhat order on S-n when d equals 2 and to the lattice of partitions of a d-set when n equals 2. (C) 2000 Academic Press.

关键词： complete flag flag manifold permutation permutation array Bruhat order partition lattice

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Finite field constructions of combinatorial arrays

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DESIGNS CODES AND CRYPTOGRAPHY 2016年第1期78卷 197-219页

作者： Moura, Lucia Mullen, Gary L. Panario, Daniel Univ Ottawa Sch Elect Engn & Comp Sci Ottawa ON K1K 6N5 Canada Penn State Univ Dept Math University Pk PA 16802 USA Carleton Univ Sch Math & Stat Ottawa ON K1S 5B6 Canada

We survey a number of topics and constructions of combinatorial arrays based on finite fields. These combinatorial objects include orthogonal arrays, covering arrays, ordered orthogonal arrays, permutation arrays, fre... 详细信息

关键词： Orthogonal array Covering array permutation array Frequency permutation array Hypercubes Costas arrays

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New Lower Bounds for permutation Codes Using Linear Block Codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2020年第7期66卷 4019-4025页

作者： Micheli, Giacomo Neri, Alessandro Univ S Florida Dept Math Tampa FL 33620 USA INRIA Saclay Ile de France F-91120 Palaiseau France

In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an [n,k,d](q) linear block code, we are able to prove the existence of a permutation code in the symmetric group of degree n, having minimum distance at least d and large cardinality. With our technique, we obtain new lower bounds for permutation codes that enhance the ones in the literature and provide asymptotic improvements in certain regimes of length and distance of the permutation code.

关键词： Parity check codes Hamming distance Hamming weight Generators Linear codes Symmetric matrices permutation code powerline communications linear block code maximum distance separable (MDS) code almost MDS code permutation array

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Bounds on permutation codes of distance four

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JOURNAL OF ALGEBRAIC COMBINATORICS 2010年第1期31卷 143-158页

作者： Dukes, P. Sawchuck, N. Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada

A permutation code of length n and distance d is a set I" of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x,yaI" is at least d. In this note, we determine some new results on the maximum size of a permutation code with distance equal to 4, the smallest interesting value. The upper bound is improved for almost all n via an optimization problem on Young diagrams. A new recursive construction improves known lower bounds for small values of n.

关键词： Symmetric group permutation code permutation array Characters Young diagram Linear programming

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The Construction of permutation Group Codes for Communication Systems: Prime or Prime Power?

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IEEE ACCESS 2020年 8卷 69953-69966页

作者： Peng, Li Chen, Sijia Guo, Shuxia Huazhong Univ Sci & Technol Wuhan Natl Lab Optoelect Sch Elect Informat & Commun Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Elect Informat & Commun Wuhan 430074 Peoples R China Northwestern Polytech Univ Sci & Technol UAV Lab Xian 710065 Peoples R China

This paper focuses on correcting a theorem relating to the construction of permutation group codes (PGCs). The theorem in question assumed that affine transformation could be used to enumerate all the code words of a permutation array with a minimum Hamming distance (MHD) of n 1 for any n > 1. This assumption was founded upon the proposition that, if the code length, n, is a prime power, then the maximum cardinality of the code will be n(n - 1) and its MHD will be n - 1. However, two typical algebraic methods, one relying on affine transformation and another upon the composite operation of two small subgroups of a symmetric group, can violate this proposition. This is because it is only when n is a prime rather than a prime power that they can enumerate all the code words of an (nI n(n - 1);n - 1)-PGC. By investigating how the range of n impacts upon the cardinality and MHD of a code, we provide a corrective theorem that stipulates the construction of (p(q);p(2q)(1 - 1/p);p(q)(1- 1/p))-PGCs when n = p(q) is a prime power, where p is a prime and q > 1. On the basis of this theorem, and under the condition of n being the power of 2, we construct a (2(q);2(2q-1);2(q-1))-PGC and present an encoder that can map a k-bit binary information sequence to an n D 22q-dimension permutation code word. The natural array structure of 2(q);2(2q-1);2(q-1))-PGCs makes them especially well-suited to forming the basis of low-complexity encoders. We present simulation-based experiments that show that, as the code length increases, the performance of these codes improves. The best performance is for a (16;128;8)-PGC, which can achieve -3.8 dB with a word error rate of 10(-7).

关键词： Magnetohydrodynamics Interference Hardware Hamming distance Channel coding Wireless communication Channel coding error correcting code permutation array permutation group code mapping encoder

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