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<p>We study the arithmetic autocorrelation of binary sequences generated by a feedback with carry shift register. We find necessary and sufficient conditions for the existence of families of such sequences with ideal arithmetic autocorrelation for arbitrary connection integer <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11122_2025_5121_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$q$</EquationSource> </InlineEquation>. Under these conditions, any pair of cyclically different sequences with connection integer <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11122_2025_5121_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$q$</EquationSource> </InlineEquation> also has ideal arithmetic crosscorrelation.</p>

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On the Ideal Arithmetic Autocorrelation of Binary FCSR Sequences

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • V. A. Edemskiy

摘要

We study the arithmetic autocorrelation of binary sequences generated by a feedback with carry shift register. We find necessary and sufficient conditions for the existence of families of such sequences with ideal arithmetic autocorrelation for arbitrary connection integer $q$ . Under these conditions, any pair of cyclically different sequences with connection integer $q$ also has ideal arithmetic crosscorrelation.