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Randomness and Representation of Span n Sequences

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Sequences, Subsequences, and Consequences

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4893))

Abstract

Any span n sequences can be regarded as filtering sequences. From this observation, new randomness criteria for span n sequences are proposed. It is proved that the feedback function of a span n sequence can be represented as a composition of its trace representation, or equivalently, its discrete Fourier transform, and a permutation from the state space of the sequence to the multiplicative group of the finite field GF(2n), and vice versa. Significant enhancements for randomness of span n sequences, so that de Bruijn sequences, are illustrated by some examples.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

    Guang Gong

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  1. Guang Gong
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Solomon W. Golomb Guang Gong Tor Helleseth Hong-Yeop Song

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Gong, G. (2007). Randomness and Representation of Span n Sequences. In: Golomb, S.W., Gong, G., Helleseth, T., Song, HY. (eds) Sequences, Subsequences, and Consequences. Lecture Notes in Computer Science, vol 4893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77404-4_19

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  • DOI: https://doi.org/10.1007/978-3-540-77404-4_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77403-7

  • Online ISBN: 978-3-540-77404-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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