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On equivalence of negaperiodic Golay pairs

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Abstract

Associated pairs as defined by Ito (J Algebra 234:651–663, 2000) are pairs of binary sequence of length 2t satisfying certain autocorrelation properties that may be used to construct Hadamard matrices of order 4t. More recently, Balonin and Doković (Inf Control Syst 5:2–17, 2015) use the term negaperiodic Golay pairs. We define extended negaperiodic Golay pairs and prove a one-to-one correspondence with central relative (4t, 2, 4t, 2t)-difference sets in dicyclic groups of order 8t. We present a new approach for computing negaperiodic Golay pairs up to equivalence, and determine conditions where equivalent pairs correspond to equivalent Hadamard matrices. We complete an enumeration of negaperiodic Golay pairs of length 2t for \(1 \le t \le 10\), and sort them into equivalence classes. Some structural properties of negaperiodic Golay pairs are derived.

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Acknowledgements

This work has been supported in part by Croatian Science Foundation under the project 1637. Parts of this work appeared in the author’s Ph.D. thesis written under the supervision of Professor Dane Flannery and was supported by the Irish Research Council (Government of Ireland Postgraduate Scholarship) and National University of Ireland, Galway (Hardiman Fellowship).

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  1. Department of Mathematics, University of Rijeka, Rijeka, Croatia

    Ronan Egan

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  1. Ronan Egan
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Correspondence to Ronan Egan.

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Communicated by K. T. Arasu.

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Egan, R. On equivalence of negaperiodic Golay pairs. Des. Codes Cryptogr. 85, 523–532 (2017). https://doi.org/10.1007/s10623-016-0320-6

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  • DOI: https://doi.org/10.1007/s10623-016-0320-6

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