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Nonexistence of a Kind of Generalized Perfect Binary Array

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Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

Generalized perfect binary array(GPBA) is a useful tool in the construction of perfect binary arrays. By investigating the character values of corresponding relative difference sets, we obtain some nonexistence results of GPBAs. In particular, we show that no GPBA(2,2,p n) of any type z exists for n=1 and any odd prime p, or for any n and any odd prime \(p\not\equiv 1 (mod{8})\). For the case p=2, there exists a GPBA(2,2,2n) of type z=(z 1,z 2,z 3) if and only if z=(0,0,0) and n=0,2,4, or z≠(0,0,0) with z 3=0 and 0≤n≤5, with z 3=1 and 0≤n≤3.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, 450052, Zhengzhou, China

    Zhang Xiyong

  2. Department of Applied Mathematics, Information Engineering University, 450002, Zhengzhou, China

    Zhang Xiyong & Han Wenbao

  3. School of Computer Science Engineering, Beihang University, 100083, Beijing, China

    Guo Hua

Authors
  1. Zhang Xiyong
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  2. Guo Hua
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  3. Han Wenbao
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Guang Gong

  2. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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© 2006 Springer-Verlag Berlin Heidelberg

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Xiyong, Z., Hua, G., Wenbao, H. (2006). Nonexistence of a Kind of Generalized Perfect Binary Array. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_26

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  • DOI: https://doi.org/10.1007/11863854_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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