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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Dimopoulou, Melpomeni Antonini, Marc Barbry, Pascal Appuswamy, Raja Univ Cote dAzur I3S CNRS UMR 7271 Nice France Univ Cote dAzur IPMC CNRS UMR 7275 Nice France Eurecom Campus SophiaTech Biot France

ISBN: (纸本)9781509066315

The exponential increase of digital data that is being generated every year along with the capacity and durability limits of conventional storage devices are raising one of the greatest challenges for the field of data storage. The use of DNA for digital data archiving is a very promising alternative as the biological properties of the DNA molecule allow the storage of a huge amount of information into a very limited volume while also promising data longevity for centuries or even longer. In this paper we present a comparative study of our work with the state of the art solutions, and show that our solution is competitive.

关键词： DNA coding data storage quaternary code sequencing noise robustness

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An Algorithm of Neighbor Finding on Sphere Triangular Meshes with quaternary code

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Geo-Spatial Information Science 2008年第2期11卷 86-89页

作者： Sun Wenbin Zhao Xuesheng School of Resource and Safety Engineering China University of Mining and Technology （Beijing） D11 Xueyuan Road Beijing 100083 China

The characteristic of quaternary codes is analyzed. The rule of distinguishing triangle direction is given out. An algorithm of neighbor finding by decomposing the quaternary code from back to front is presented in this paper. The contrastive analysis of time complexity between this algorithm and Bartholdi＇s algorithm is approached. The result illustrates that the average consumed time of this algorithm is about 23.66% of Bartholdi＇s algorithm.

关键词： quaternary code neighbor finding sphere triangular mesh

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Constructing optimal few weight quaternary linear codes via multivariable functions

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2025年第1期17卷 57-85页

作者： Hyun, Jong Yoon Jeong, Jihye Lee, Yoonjin Konkuk Univ Glocal Campus268Chungwon Daero Chungjusi 27478 Chungcheongbug South Korea Ewha Womans Univ Dept Math 52Ewhayeodae Gil Seoul 03760 South Korea

We construct new infinite families of (near) Plotkin-optimal 2-weight or 3-weight codes over Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document} by using the shortening method. Furthermore, we completely determine the Lee weight distributions of our shortened codes. To achieve our goal, we use certain families of multivariable functions, and we interpret a shortening method followed by puncturing in terms of multivariable functions. According to this interpretation, we find explicit criteria for the shortened codes to have fewer Lee weights and larger minimum Lee weights after the shortening process. As our contribution, we emphasize that non-Plotkin-optimal code families are converted to Plotkin-optimal code families after the shortening process by using our main results. Furthermore, we produce new infinite families of (near) Plotkin-optimal 2-weight or 3-weight codes over Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document}, which extend the database of linear codes over Z4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}_4$$\end{document}.

关键词： Shortening Optimal code quaternary code Few weight Multivariable function

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quaternary codes and Their Binary Images

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第7期70卷 4759-4768页

作者： Wu, Yansheng Li, Chao Zhang, Lin Xiao, Fu Nanjing Univ Posts & Telecommun Sch Comp Sci Nanjing 210023 Peoples R China

Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun et al. Building upon their research, in this paper more linear codes over the ring Z(4) are constructed by simplicial complexes. Specifically, the Lee weight distributions of the resulting quaternary codes are determined and two infinite families of four-Lee-weight quaternary codes are obtained. Compared to the databases of Z(4 )codes by Aydin et al., at least nine new quaternary codes are found. Thanks to the special structure of the defining sets, we have the ability to determine whether the Gray images of certain obtained quaternary codes are linear or not. This allows us to obtain two infinite families of binary nonlinear codes and one infinite family of binary minimal linear codes. Furthermore, utilizing these minimal binary codes, some secret sharing schemes as a byproduct also are established.

关键词： codes Linear codes codecs Cryptography Telecommunications Computer science Hamming weight quaternary code simplicial complex gray map binary nonlinear code minimal code secret sharing scheme

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Two Infinite Families of quaternary codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第12期70卷 8723-8733页

作者： Wu, Yansheng Li, Bowen Fan, Weibei Xiao, Fu Nanjing Univ Posts & Telecommun Sch Comp Sci Nanjing 210023 Peoples R China

Recently, Hyun et al. have utilized simplicial complexes to construct several infinite families of binary minimal and optimal linear codes. Building upon their work, we draw inspiration and extend their research by constructing codes over the ring Z(4) with the aid of simplicial complexes. In this paper, we present two infinite families of quaternary codes, one of which is linear while the other is nonlinear. We analyze the Lee weight distributions of the resulting quaternary codes and compare them with the existing database of Z(4) codes. Our findings reveal the discovery of several new quaternary codes. Furthermore, we also provide two classes of binary codes that can be obtained from these quaternary codes using the Gray map.

关键词： quaternary code Lee weight distribution Gray map binary code

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Classification of Extremal Self-Dual quaternary codes of Lengths 30 and 32

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IEEE TRANSACTIONS ON INFORMATION THEORY 2013年第4期59卷 2352-2358页

作者： Kim, Hyun Jin Lee, Yoonjin Ewha Womans Univ Inst Math Sci Seoul 120750 South Korea Ewha Womans Univ Dept Math Seoul 120750 South Korea

We classify extremal Hermitian self-dual quaternary codes of lengths 30 and 32 with an automorphism of odd prime order. We prove that there exists exactly one extremal Hermitian self-dual quaternary code with a nontrivial automorphism of odd prime order, up to equivalence;the order of its automorphism group is 36 540. In fact, this code is equivalent to the extended quadratic residue code. We also prove that there exists no extremal Hermitian self-dual quaternary code with a nontrivial automorphism of odd prime order.

关键词： Automorphism extremal code quaternary code self-dual code

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Theory of J-characteristics of four-level designs under quaternary codes

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 439卷

作者： Fang, Xiangyu Li, Hongyi Ou, Zujun Jishou Univ Coll Math & Stat Jishou 416000 Peoples R China Hunan Inst Traff Engn Hengyang 421001 Peoples R China

The J-characteristics play an instrumental role in the development of generalized resolution and minimum aberration criteria for two-level designs. In this paper, the concept of J-characteristics is naturally generalized to four-level designs via quaternary codes, which maps the four-level designs to two-level designs. Based on the relationship between the minimum G2-aberration criterion of two-level design and the generalized minimum aberration criterion of its projection designs, the properties of J-characteristics of four-level designs are explored. The relationship between J-characteristics of four-level design and J-characteristics of corresponding effective two-level sub-designs is built. The generalized resolution, confounding frequency vector and B-vector of four-level design are respectively defined based on the J-characteristics and their upper bounds, and minimum G-aberration and minimum G2-aberration criteria of four-level design are proposed, which are useful to assess the goodness of four-level designs.(c) 2023 Published by Elsevier B.V.

关键词： Four-level designs Minimum G -aberration quaternary code J-characteristics MinimumG2-aberration

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3-Designs from all Z₄-Goethals-like codes with block size 7 and 8

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FINITE FIELDS AND THEIR APPLICATIONS 2007年第4期13卷 815-827页

作者： Lahtonen, Jyrki Ranto, Kalle Vehkalahti, Roope Univ Turku Dept Math FIN-20014 Turku Finland Turku Ctr Comp Sci TUCS FIN-20014 Turku Finland

We construct a family of simple 3-(2(m), 8, 14(2(m) - 8)/3) designs, with odd m >= 5, from all Z(4)-Goethals-like codes G(k). In addition, these designs imply the existence of other design families with the same parameters as the designs constructed from the Z(4)-Goethals code G(1), i.e. the designs with a block size 7 by Shin, Kumar, and Helleseth and the designs with a block size 8 by Ranto. In the existence proofs we count the number of solutions to certain systems of equations over finite fields and use properties of Dickson and linearized polynomials. Also, the nonequivalence of the designs from different Goethals-like codes is considered. (c) 2006 Elsevier Inc. All rights reserved.

关键词： t-Design Goethals code quaternary code Dickson polynomial linearized polynomial

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A sequence of unique quaternary Griesmer codes

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DESIGNS codeS AND CRYPTOGRAPHY 2004年第1期33卷 71-85页

作者： Ward, HN Univ Virginia Dept Math Charlottesville VA 22904 USA

This paper establishes that there is no [98, 5, 72](4) code. Such a code would meet the Griesmer bound and the weights of its codewords would all be divisible by 4. The proof of nonexistence uses the uniqueness of codes with parameters [n, 4, n - 5](4), 14 less than or equal to n less than or equal to 17. The uniqueness of these codes for n greater than or equal to 15 had been established geometrically by others;but it is rederived here, along with that of the [14, 4, 9](4) code, by exploiting the Hermitian form obtained when the weight function is read modulo 2.

关键词： Griesmer bound quaternary code Hermitian form divisible code residual code MacWilliams identities

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Infinite families of 3-designs from Z₄-Goethals codes with block size 8

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2002年第3期15卷 289-304页

作者： Ranto, K TUCS Turku Ctr Comp Sci FIN-20520 Turku Finland

We construct several new families of simple 3-designs from codewords of the Z(4)-Goethals codes. These designs have parameters 3-(2(m), 8, lambda) with odd m greater than or equal to 5. The smallest design has lambda = 14(2(m)-8)/3, and the others are corollaries of this and some previously known designs. In the existence proofs we analyze the low-weight codewords and count the umber of solutions to certain systems of equations over finite fields.

关键词： t-design Goethals code quaternary code Kloosterman sum

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