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<p>In many applications it is very important to know that the family of pseudorandom binary lattices has a “rich" and “complex" structure. To handle this requirement, Gyarmati, Mauduit and Sárközy introduced the cross-combined measure and presented important constructions of large families of binary lattices with optimal or nearly optimal cross-combined measures. In this paper we study the cross-combined measure of families based on polynomials in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_644_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_p\left[ x, y\right] \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">F</mi> <mi>p</mi> </msub> <mfenced close="]" open="["> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> and additive character in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_644_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>, and give large families of binary lattices with good cross-combined measures.</p>

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Cross-combined measures of families of binary lattices

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Huaning Liu,
  • Jingyi Hao

摘要

In many applications it is very important to know that the family of pseudorandom binary lattices has a “rich" and “complex" structure. To handle this requirement, Gyarmati, Mauduit and Sárközy introduced the cross-combined measure and presented important constructions of large families of binary lattices with optimal or nearly optimal cross-combined measures. In this paper we study the cross-combined measure of families based on polynomials in \(\mathbb {F}_p\left[ x, y\right] \) F p x , y and additive character in \(\mathbb {F}_p\) F p , and give large families of binary lattices with good cross-combined measures.