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On the existence of periodic complementary binary sequences

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Abstract

Using the connection between periodic complementary binary sequences and difference families given by Bömer and Antweiler [2], we use number theoretic techniques to obtain necessary conditions for their existence when two or three sequences are involved. Our results provide theoretical proof for the nonexistence of PCS3 20(a i) and settle the open case PCS2 36(a i) of [2], negatively.

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References

  1. T. Beth, D. Jungnickel, and H. Lenz, Design Theory, Zurich: Bibliographisches Institute 1985.

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  2. L. Bömer and M. Antweiler, Periodic complementary binary sequences, IEEE Trans. Inform. Theory, Vol. 36, (1990), pp. 1487–1494.

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  3. S. Eliahou, M. Kervaire, and B. Saffari, A new restriction on the lengths of Golay complementary sequences, J. Combin. Theory Ser. A Vol. 55, (1990), pp. 49–59.

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  4. S.L. Ma, Polynomial addition sets, Ph.D. Thesis, University of Hong Kong, 1985.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wright State University, 45435, Dayton, Ohio, USA

    K. T. Arasu & Qing Xiang

Authors
  1. K. T. Arasu
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  2. Qing Xiang
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Additional information

Communicated by D. Jungnickel

Research partially supported by National Security Agency grant #MDA 904-90-H-4008.

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Arasu, K.T., Xiang, Q. On the existence of periodic complementary binary sequences. Des Codes Crypt 2, 257–262 (1992). https://doi.org/10.1007/BF00141970

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  • DOI: https://doi.org/10.1007/BF00141970

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