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<p>The trace representation of sequences is useful for implementing the generator of sequences and analyzing their cryptographic properties. In this paper, we focus on investigating the trace representation for a family of generalized cyclotomic binary sequences with period <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1638_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(p^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>p</mi> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. On the basis of the properties of the generalized cyclotomic classes, a trace representation of this family of sequences is obtained by computing the discrete Fourier transform of the sequences, whenever <i>p</i> is a non-Wieferich prime. In addition, a known result on the linear complexity for this family of sequences is derived from its trace representation.</p>

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Trace representation of a family of generalized cyclotomic binary sequences with period \(p^n\)

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Zibi Xiao,
  • Yaya Ye,
  • Zhiye Yang,
  • Xiangyong Zeng

摘要

The trace representation of sequences is useful for implementing the generator of sequences and analyzing their cryptographic properties. In this paper, we focus on investigating the trace representation for a family of generalized cyclotomic binary sequences with period \(p^n\) p n . On the basis of the properties of the generalized cyclotomic classes, a trace representation of this family of sequences is obtained by computing the discrete Fourier transform of the sequences, whenever p is a non-Wieferich prime. In addition, a known result on the linear complexity for this family of sequences is derived from its trace representation.