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A direct construction of even length ZCPs with large ZCZ ratio

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Abstract

This paper presents a direct construction of aperiodic q-ary (q is a positive even integer) even length Z-complementary pairs (ZCPs) with large zero-correlation zone (ZCZ) width using generalised Boolean functions (GBFs). The applicability of ZCPs increases with the increasing value of ZCZ width, which plays a significant role in reducing interference in a communication system with asynchronous surroundings. For q = 2, the proposed ZCPs reduce to even length binary ZCPs (EB-ZCPs). However, to the best of the authors’ knowledge, the highest ZCZ ratio for even length ZCPs which are directly constructed to date using GBFs is 3/4. In the proposed construction, we provide even length ZCPs with ZCZ ratios 5/6 and 6/7, which are the largest ZCZ ratios achieved to date through direct construction.

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Authors and Affiliations

  1. Department of Mathematics, IIT Patna, Bihta, Bihar, 801006, Patna, India

    Praveen Kumar & Subhabrata Paul

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

    Palash Sarkar

  3. Department of Electrical Communication Engineering, IISc Bangalore, CV Raman Rd, Bengaluru, 560012, Karnataka, India

    Sudhan Majhi

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  1. Praveen Kumar
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  2. Palash Sarkar
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  3. Sudhan Majhi
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  4. Subhabrata Paul
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Correspondence to Sudhan Majhi.

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Kumar, P., Sarkar, P., Majhi, S. et al. A direct construction of even length ZCPs with large ZCZ ratio. Cryptogr. Commun. 15, 85–94 (2023). https://doi.org/10.1007/s12095-022-00589-0

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  • DOI: https://doi.org/10.1007/s12095-022-00589-0

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