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Note on Periodic Complementary Sets of Binary Sequences

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Abstract

Denote by \(PCS_p^n \) resp. \(ACS_p^n \) thecollection consisting of ordered p-tuples of binary sequences(i.e., sequences whose elements are \( \pm 1\)), each having length n, such that the sum of their periodic resp. aperiodicauto-correlation functions is a delta function. We fill many open cases inthe Bömer and Antweiler diagram [3] of the known cases where \(PCS_p^n \)exist for \(p \leqslant 12\) and \(n \leqslant 50\). In particular we show that \(PCS_2^{34} \) exist, whileit is well known [1] that \(ACS_2^{34} \) do not.

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  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Dragomiru Z. Dokovic

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  1. Dragomiru Z. Dokovic
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Dokovic, D.Z. Note on Periodic Complementary Sets of Binary Sequences. Designs, Codes and Cryptography 13, 251–256 (1998). https://doi.org/10.1023/A:1008245823233

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