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Large families of sequences for CDMA, frequency hopping, and UWB

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Abstract

This paper generalizes three constructions of families of sequences with bounded off peak correlation with application to Code Division Multiple Access (CDMA), frequency hopping, and Ultra Wide Band (UWB). These new families present flexible family sizes and sequence lengths, making them well suited to wireless communications and Multiple Input Multiple Output (MIMO) radar. In particular, we show that the generalized Kamaletdinov I construction offers the lowest off-peak correlation for a given family size. For the two smallest family sizes, this construction asymptotically matches the performance of the small Kasami set and Gold codes, respectively. Among other properties, it has one of the slowest off-peak correlation growth of all known constructions, increasing proportionally to the logarithm of the family size and generates frequency and time hopping sequences.

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Acknowledgements

We thank four anonymous referees for their helpful suggestions which have improved the paper. Domingo Gómez-Pérez thanks Andrew Tirkel and Udaya Parampalli for their hospitality during a productive research stay in Melbourne.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, University of Cantabria, Santander, Spain

    Domingo Gómez-Pérez & Ana I. Gómez

  2. Scientific Technology, 8 Cecil Street, Brighton East, 3187, Australia

    Andrew Tirkel

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  1. Domingo Gómez-Pérez
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  2. Ana I. Gómez
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  3. Andrew Tirkel
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Correspondence to Domingo Gómez-Pérez.

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The research of the first and second author was supported by the Spanish Ministerio de Economía y Competitividad research project MTM2014-55421-P.

This article is part of the Topical Collection on Special Issue on Sequences and Their Applications

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Gómez-Pérez, D., Gómez, A.I. & Tirkel, A. Large families of sequences for CDMA, frequency hopping, and UWB. Cryptogr. Commun. 12, 389–403 (2020). https://doi.org/10.1007/s12095-019-00399-x

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  • DOI: https://doi.org/10.1007/s12095-019-00399-x

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