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<p>In this paper, we first construct two new classes of 3-level autocorrelation binary sequences with period 4<i>N</i> by 2-level autocorrelation binary sequences with period <i>N</i>, according to two different interleaving methods. Subsequently, through the support sets of newly constructed sequences, new divisible difference sets and almost difference sets are derived using the technique of difference functions. Finally, a class of new difference sets is defined, that is, special partial direct product difference sets (SPDPDS), and the equivalence between the constructed 3-level autocorrelation binary sequences and this class of difference sets is revealed.</p>

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Constructions of divisible difference sets, almost difference sets and special partial direct product difference sets from binary sequences

  • 期刊论文

  • 发表日期：

    2025年4月30日

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  • Yan Wang,
  • Danyang Li,
  • Nian Li,
  • Jiayi Fan

摘要

In this paper, we first construct two new classes of 3-level autocorrelation binary sequences with period 4N by 2-level autocorrelation binary sequences with period N, according to two different interleaving methods. Subsequently, through the support sets of newly constructed sequences, new divisible difference sets and almost difference sets are derived using the technique of difference functions. Finally, a class of new difference sets is defined, that is, special partial direct product difference sets (SPDPDS), and the equivalence between the constructed 3-level autocorrelation binary sequences and this class of difference sets is revealed.