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The \(\ell \) -sequences are a family of pseudorandom sequences produced by feedback with carry shift registers. They have ideal arithmetic auto-correlation and many other desirable pseudorandom properties. Half- \(\ell \) -sequences are an extension of \(\ell \) -sequences and studied in the recent decade. In this work, we prove that certain half- \(\ell \) -sequences with special connection integers might have large arithmetic auto-correlations, unlike \(\ell \) -sequences.

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Arithmetic Autocorrelation of Certain Binary Half- \(\ell \) -Sequences

  • 会议论文

  • 发表日期：

    2026年

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  • Lingmei Xiao,
  • Vladimir Edemskiy

摘要

The \(\ell \) -sequences are a family of pseudorandom sequences produced by feedback with carry shift registers. They have ideal arithmetic auto-correlation and many other desirable pseudorandom properties. Half- \(\ell \) -sequences are an extension of \(\ell \) -sequences and studied in the recent decade. In this work, we prove that certain half- \(\ell \) -sequences with special connection integers might have large arithmetic auto-correlations, unlike \(\ell \) -sequences.