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On some batch code properties of the simplex code

DESIGNS codeS AND CRYPTOGRAPHY 2023年第5期91卷 1595-1605页

作者： Hollmann, Henk D. L. Khathuria, Karan Riet, Ago-Erik Skachek, Vitaly Univ Tartu Inst Comp Sci EE-50409 Tartu Estonia Univ Tartu Inst Math & Stat EE-50409 Tartu Estonia

The binary k-dimensional simplex code is known to be a 2(k-1)-batch code and is conjectured to be a 2(k-1)-functional batch code. Here, we offer a simple, constructive proof of a result that is "in between" these two properties. Our approach is to relate these properties to certain (old and new) additive problems in finite abelian groups. We also formulate a conjecture for finite abelian groups that generalizes the above-mentioned conjecture.

关键词： Batch codes simplex code Switch codes Functional batch code Finite abelian groups

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Raman DTS Based on OTDR Improved by Using Gain-Controlled EDFA and Pre-Shaped simplex code

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IEEE SENSORS JOURNAL 2017年第11期17卷 3346-3353页

作者： Rosolem, Joao Batista Bassan, Fabio Renato de Freitas, Daiane Eliene Salgado, Felipe Cezar CPqD Res & Dev Ctr Telecommun BR-13086902 Campinas SP Brazil Friedrich Schiller Univ Jena Fac Phys & Astron D-07743 Jena Germany

This paper described a distributed temperature sensing (DTS) system based on Raman scattering using pre-shaped simplex code (S code) with erbium-doped fiber amplifiers (EDFAs) transient effects suppression techniques. We investigated these techniques to mitigate the waveform distortion caused by the EDFA when DTS uses S code in an optical time-domain reflectometer (OTDR). We tested the DTS experimentally using two EDFA's transient effects suppression techniques: automatic gain control and pre-shaped S code pulses. The performance of these two techniques working simultaneously was compared with the standard S code technique. In the experimental setup, we tested code word lengths from 3 to 127 b with 100-ns pulsewidth. The temperature measurement demonstration was done in reaches of 40 and 50 km, and in a repeated system of 62 km using standard single-mode fiber and commercial OTDR and EDFA modules, which were properly adapted to this application. Results show that EDFA's transient effects suppression techniques allow increasing the reach of DTS using short S code sequences, reducing the complexity and the processing time.

关键词： DTS distributed temperature sensing simplex code transient effects suppression gain controlled EDFA

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The complete hierarchical locality of the punctured simplex code

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DESIGNS codeS AND CRYPTOGRAPHY 2021年第1期89卷 105-125页

作者： Grezet, Matthias Hollanti, Camilla Aalto Univ Dept Math & Syst Anal Espoo 00076 Finland

This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simp... 详细信息

关键词： Hierarchical locality Alphabet-dependent bound simplex code Matroid theory

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Optimal (r, δ)-Locally Repairable codes From simplex code and Cap code

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IEEE ACCESS 2020年 8卷 215414-215418页

作者： Fu, Qiang Li, Ruihu Yang, Sen Air Force Engn Univ Dept Basic Sci Xian 710051 Peoples R China

Locally repairable codes (LRCs) are implemented in distributed storage systems (DSSs) due to their low repair overhead. A linear code C is said to have (r, delta)-locality if for each coordinate i, there exists a punctured subcode of C with support containing i, whose length is at most r + delta - 1 and whose minimum distance is at least delta. An LRC is called optimal if its minimum distance attains Singleton-type bound was proposed. In this letter, optimal LRCs are considered. We first determine (r, delta)-locality of three dimensional simplex code, then using anticode strategy, a class of [3q, 3, 2q - 1](q) LRCs with (2, q) locality are derived for general q. Finally, using an ovoid in PG(3;q), we construct [q(2)+1, 4, q(q-1)](q) and [4q-4, 3q-5](q) LRCs with r = 3 and delta = q - 1. All LRCs constructed in this letter attain the Singleton-type bound.

关键词： codecs Generators Spread spectrum communication Linear codes Maintenance engineering Licenses Interpolation Singleton-type bound simplex code optimal locally repairable codes cap code

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Raman-based Distributed Temperature Sensor using simplex code and Gain Controlled EDFA 24

Raman-based Distributed Temperature Sensor using Simplex Cod...

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24th International Conference on Optical Fibre Sensors (OFS)

作者： Bassan, F. R. Penze, R. S. Leonardi, A. A. Fracarolli, J. P. V. Floridia, C. Rosolem, J. B. Fruett, F. CPqD Fdn R Ricardo Benetton Martins S-N BR-13086902 Campinas SP Brazil Univ Estadual Campinas BR-13083852 Campinas SP Brazil

ISBN: (纸本)9781628418392

In this work we present a comparison between simplex coded and optical amplified simplex coded Raman based Distributed Temperature Sensing (DTS). An increase in performance is demonstrated using erbium doped fiber amplifier (EDFA) with proper gain control scheme that allows a DTS operates with simplex code. Using 63-bit simplex code and gain controlled EDFA we demonstrated the temperature resolution and dynamic range improvement in 16 degrees C @ 10 km and 4 dB, respectively.

关键词： DTS simplex code Gain Controlled EDFA AGC

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Using the simplex code to Construct Relative Difference Sets in 2-groups

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Designs, codes, and Cryptography 1997年第3期11卷 267-277页

作者： Davis, James A. Sehgal, Surinder K. University of Richmond Department of Mathematics Richmond VA 23173 United States Ohio State University Columbus OH 43210 United States

Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of rela... 详细信息

Relative Difference Sets with the parameters (2^a, 2^b, 2^a, 2^a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The simplex code is used in the construction.

关键词： 2-groups Relative difference sets simplex code

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Bstj 45: 8. October 1966: on the Optimality of the Regular simplex code. (Landau, H.J.;Slepian, David)

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2016年

Bstj 45: 8. October 1966: on the Optimality of the Regular simplex code. (Landau, H.J.; Slepian, David) by published by

关键词： (landau, bell system biorthogonal code cap code code points code. david) denote equal energy h.j. hyperplane monotone monotone decreasing nonnegative monotone optimal regular regular simplex simplex simplex code sin spherical spherical cap system technical

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Symmetric (15,8,4)-designs in terms of the geometry of binary simplex codes of dimension 4

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DESIGNS codeS AND CRYPTOGRAPHY 2025年 1-15页

作者： Pankov, Mark Petelczyc, Krzysztof Zynel, Mariusz Univ Warm & Mazury Olsztyn Fac Math & Comp Sci SLoneczna 54 PL-10710 Olsztyn Poland Univ Bialystok Fac Math Ciolkowskiego 1M PL-15245 Bialystok Poland

Let n=2k-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=2<^>k-1$$\end{document} and m=2k-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=2<^>{k-2}$$\end{document} for a certain k >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\ge 3$$\end{document}. Consider the point-line geometry of 2m-element subsets of an n-element set. Maximal singular subspaces of this geometry correspond to binary simplex codes of dimension k. For k >= 4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\ge 4$$\end{document} the associated collinearity graph contains maximal cliques different from maximal singular subspaces. We investigate maximal cliques corresponding to symmetric (n, 2m, m)-designs. The main results concern the case k=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=4$$\end{document} and give a geometric interpretation of the five well-known symmetric (15, 8, 4)-designs.

关键词： Point-line geometry Collinearity graph simplex code Symmetric design

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Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

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JOURNAL OF COMBINATORIAL THEORY SERIES A 2025年 214卷

作者： Shi, Minjia Li, Shitao Helleseth, Tor Kim, Jon-Lark Anhui Univ Sch Math Sci Key Lab Intelligent Comp & Signal Proc Minist Educ Hefei Anhui Peoples R China Anhui Univ Sch Math Sci Hefei Peoples R China Univ Bergen Dept Informat Bergen Norway Sogang Univ Dept Math Seoul South Korea Sogang Univ Inst Math & Data Sci Seoul South Korea

The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing the Solomon-Stiffier codes. As a result, we reduce a problem with an infinite number of cases to a finite number of cases. Second, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code. Using such a characterization, we completely determine the exact value of dso(n, 7), where dso(n, k) denotes the largest minimum distance among all binary self-orthogonal [n, k] codes. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Binary self-orthogonal code simplex code First order Reed-Muller code Solomon-Stiffler code Belov code

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Point-line geometries related to binary equidistant codes

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JOURNAL OF COMBINATORIAL THEORY SERIES A 2025年 210卷

作者： Pankov, Mark Petelczyc, Krzysztof Zynel, Mariusz Univ Warmia & Mazury Fac Math & Comp Sci Sloneczna 54 PL-10710 Olsztyn Poland Univ Bialystok Fac Math Ciolkowskiego 1M PL-15245 Bialystok Poland

Point-line geometries whose singular subspaces correspond to binary equidistant codes are investigated. The main result is a description of automorphisms of these geometries. In some important cases, automorphisms induced by non-monomial linear automorphisms surprisingly arise. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： simplex code Equidistant code Pasch configuration Cremona-Richmond configuration Partial Steiner triple system

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