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PSWF-based direct-sequence UWB transmission using orthogonal ternary code sets

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2006年第11期E89A卷 3042-3049页

作者： Cho, Chihong Zhang, Honggang Nakagawa, Masao Keio Univ Fac Sci & Technol Yokohama Kanagawa 2238522 Japan Create Net I-38100 Trento Italy

An enhanced Ultra Wideband (UWB) signaling scheme that employs PSWF (Prolate Spheroidal Wave Functions)-based orthogonal chip pulses and ternary complementary code sets is proposed for Direct-Sequence (DS) UWB systems. Every information bit of each user is modulated and transmitted over a set of parallel sequences of PSWF-based orthogonal chip pulses and are further assigned to a ternary complementary code set with additional zero padding if necessary: Moreover, the ternary complementary code sets are generated to be mutually orthogonal and assigned to any pair of multiple users. Hence, the mitigation of multipath interference as well as multiple user interference (MUl) can be expected. Furthermore, the ternary code length can be greatly shortened by taking advantage of pulse and code orthogonality. Thus, the proposed transmission scheme is especially suitable for high data rate DS-UWB systems that offer very high flexibility.

关键词： Ultra Wideband UWB Prolate Spheroidal Wave Functions PSWF direct sequence ternary code S-V channel model

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PSWF-based Direct-Sequence UWB Transmission Using Orthogonal ternary code Sets

PSWF-based Direct-Sequence UWB Transmission Using Orthogonal...

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3rd IEEE Consumer Communications and Networking Conference

作者： Cho, Chihong Nakagawa, Masao Zhang, Honggang Zhou, Zheng Keio Univ Dept Informat & Comp Sci Yokohama Kanagawa 223 Japan Create Net Trento Italy Beijing Univ Sch Telecommun Engn Beijing 100871 Peoples R China

ISBN: (纸本)9781424400850

An enhanced Ultra Wideband (UWB) signaling scheme employing PSWF (Prolate Spheroidal Wave Functions)based orthogonal chip pulses and ternary complementary code sets is proposed for Direct-Sequence (DS) UWB systems. Every information bit of each user is modulated and transmitted over a set of parallel sequences of PSWF-based orthogonal chip pulses and are further assigned to a ternary complementary code set with additional zero padding if necessary. Moreover, the ternary complementary code sets are generated to be mutually orthogonal and assigned to any pair of multiple users. Hence, the mitigation of multipath interference as well as Multiple User Interference (MUI) can be expected. Furthermore, the ternary code length can be possibly designed to be much shorter by taking advantage of the pulse and code orthogonality. Thus, the proposed transmission scheme is especially suitable for high data rate DS-UWB systems for achieving much more flexibilities.

关键词： Ultra Wideband UWB Prolate Spheroidal Wave Functions PSWF direct sequence ternary code S-V channel model

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On a class of optimal constant weight ternary codes

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DESIGNS codeS AND CRYPTOGRAPHY 2023年第1期91卷 45-54页

作者： Kharaghani, Hadi Suda, Sho Zaitsev, Vlad Univ Lethbridge Dept Math & Comp Sci Lethbridge AB T1K 3M4 Canada Natl Def Acad Japan Dept Math Yokosuka Kanagawa 2398686 Japan

A weighing matrix W of order n = p(m+1)-1/p-1 and weight p(m) is constructed and shown that the rows of W and -W together form optimal constant weight ternary codes of length n, weight p(m) and minimum distance p(m-1) (p+3/2) for each odd prime power p and integer m >= 1 and thus A(3) (p(m+1)-1/p - 1, p(m-1)(p + 3/2), p(m)) = 2(p(m+1)-1/p - 1).

关键词： Weighing matrix ternary code Constant weight code Optimal code Johnson bound

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On the classification of certain ternary codes of length 12

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HIROSHIMA MATHEMATICAL JOURNAL 2016年第1期46卷 87-96页

作者： Araya, Makoto Harada, Masaaki Shizuoka Univ Fac Informat Dept Comp Sci Hamamatsu Shizuoka 4328011 Japan Tohoku Univ Grad Sch Informat Sci Res Ctr Pure & Appl Math Sendai Miyagi 9808579 Japan

Shimada and Zhang studied the existence of polarizations on some super-singular K3 surfaces by reducing the existence of the polarizations to that of ternary [12, 5] codes satisfying certain conditions. In this note, we give a classification of ternary [12, 5] codes satisfying the conditions. To do this, ternary [10, 5] codes are classified for minimum weights 3 and 4.

关键词： ternary code classification weight enumerator

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Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

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Applied Mathematics and Mechanics(English Edition) 2024年第7期45卷 1225-1242页

作者： Zhou HU Zhibo WEI Yan CHEN Rui ZHU School of Aerospace Engineering Beijing Institute of TechnologyBeijing100081China School of Mechanical Engineering Tianjin UniversityTianjin300350China Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education Tianjin UniversityTianjin300350China

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic ***,most of them rely on the resonant structural components,and thus are frequency-dependent and ***,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic *** on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are ***,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first ***,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative ***,the wave functions with detailed microstructures are numerically verified.

关键词： elastic metamaterial elastic wave reconfigurable design zero mode ternary code programmable refraction

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A family of optimal ternary cyclic codes from the Niho-type exponent

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FINITE FIELDS AND THEIR APPLICATIONS 2018年第Nov.期54卷 101-112页

作者： Yan, Haode Zhou, Zhengchun Du, Xiaoni Southwest Jiaotong Univ Sch Math Chengdu 610031 Sichuan Peoples R China State Key Lab Cryptol POB 5159 Beijing 100878 Peoples R China Northwest Normal Univ Coll Math & Stat Lanzhou 730070 Gansu Peoples R China

Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. The objective of this paper is to present a family of optimal ternary cyclic codes from the Niho-type exponent. Specifically, for an odd integer m and a positive integer r with 4r 1(mod m), a family of cyclic codes C-(u,C- v) of length 3(m) - 1 over GF(3) with two nonzeros beta(u) and beta(v) is studied, where beta is a generator of GF(3(m))*, u = (3(m) + 1)/2 and v = 3(r) + 2 is the ternary Niho-type exponent. The parameters of this family of cyclic codes are determined. It turns out that C-(u,C- v) is optimal with respect to the Sphere Packing bound if 9 (sic) m and otherwise almost optimal. Thanks to a recent proof of the Dobbertin-Helleseth-Kumar-Martin conjecture by Katz and Langevin, the dual of this family of cyclic codes is shown to have at most five nonzero weights. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Cyclic code Optimal code ternary code Sphere Packing bound Niho exponent

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Hadamard matrices of order 32 and extremal ternary self-dual codes

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DESIGNS codeS AND CRYPTOGRAPHY 2011年第2期58卷 203-214页

作者： Betsumiya, Koichi Harada, Masaaki Kimura, Hiroshi Yamagata Univ Dept Math Sci Yamagata 9908560 Japan Hirosaki Univ Grad Sch Sci & Technol Hirosaki Aomori 0368561 Japan Japan Sci & Technol Agcy PRESTO Kawaguchi Saitama 3320012 Japan

A ternary self-dual code can be constructed from a Hadamard matrix of order congruent to 8 modulo 12. In this paper, we show that the Paley-Hadamard matrix is the only Hadamard matrix of order 32 which gives an extremal self-dual code of length 64. This gives a coding theoretic characterization of the Paley-Hadamard matrix of order 32.

关键词： Hadamard matrix Paley-Hadamard matrix Extremal self-dual code ternary code

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On the covering radius of ternary extremal self-dual codes

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DESIGNS codeS AND CRYPTOGRAPHY 2004年第2期33卷 149-158页

作者： Harada, M Ozeki, M Tanabe, K Yamagata Univ Dept Math Sci Yamagata 9908560 Japan Univ Tsukuba Inst Math Tsukuba Ibaraki 3058571 Japan

In this paper, we investigate the covering radius of ternary extremal self-dual codes. The covering radii of all ternary extremal self-dual codes of lengths up to 20 were previously known. The complete coset weight distributions of the two inequivalent extremal self-dual codes of length 24 are determined. As a consequence, it is shown that every extremal ternary self-dual code of length up to 24 has covering radius which meets the Delsarte bound. The first example of a ternary extremal self-dual code with covering radius which does not meet the Delsarte bound is also found. It is worth mentioning that the found code is of length 32.

关键词： covering radius ternary code self-dual code

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On an open problem about a class of optimal ternary cyclic codes

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FINITE FIELDS AND THEIR APPLICATIONS 2019年 59卷 335-343页

作者： Han, Dongchun Yan, Haode Southwest Jiaotong Univ Sch Math Chengdu 610031 Sichuan Peoples R China

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem about a class of optimal ternary cyclic codes which was proposed by Ding and Helleseth [5]. Let C-(1,C-e) be a cyclic code of length 3(m) - 1 over GF(3) with two nonzeros alpha and alpha(e), where m and e are given integers, and alpha is a generator of GF(3(m))*. It is shown that C-(1,C-e) is optimal with parameters [3(m) - 1, 3(m)-1-2m, 4] if one of the following conditions is met. 1) m equivalent to 0(mod 4), m >= 4, and e = 3(m/2) + 5.2) m equivalent to 2(mod 4), m >= 6, and e = 3(m+2/2) + 5. (C) 2019 Published by Elsevier Inc.

关键词： Cyclic code Optimal code ternary code Sphere Packing bound

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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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