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<p>EvenQuads is a new card game that is a generalization of the SET game, where each card is characterized by three attributes, each taking four possible values. Four cards form a quad when, for each attribute, the values are the same, all different, or half and half. For any <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_4293_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation> cards selected from the deck of EvenQuads, it is possible to construct an error-correcting linear binary code of length <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42979_2025_4293_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation> and Hamming distance 4, where quads correspond to codewords of weight 4. Using error-correcting codes, we calculate the number of possible quads that can be formed with up to 8 cards. We also estimate the number of cards that do not contain quads for decks of different sizes. In addition, we discuss properties of error-correcting codes built on semimagic, magic, and strongly magic quad squares. This highlights a rich interplay between recreational mathematics games and coding theory and encourages others to explore similar combinatorial games for hidden connections!</p>

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EvenQuads Game and Error-Correcting Codes

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月22日

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  • Nikhil Byrapuram,
  • Hwiseo Choi,
  • Adam Ge,
  • Selena Ge,
  • Sylvia Zia Lee,
  • Evin Liang,
  • Rajarshi Mandal,
  • Aika Oki,
  • Daniel Wu,
  • Michael Yang,
  • Tanya Khovanova

摘要

EvenQuads is a new card game that is a generalization of the SET game, where each card is characterized by three attributes, each taking four possible values. Four cards form a quad when, for each attribute, the values are the same, all different, or half and half. For any \(\ell\) ℓ cards selected from the deck of EvenQuads, it is possible to construct an error-correcting linear binary code of length \(\ell\) ℓ and Hamming distance 4, where quads correspond to codewords of weight 4. Using error-correcting codes, we calculate the number of possible quads that can be formed with up to 8 cards. We also estimate the number of cards that do not contain quads for decks of different sizes. In addition, we discuss properties of error-correcting codes built on semimagic, magic, and strongly magic quad squares. This highlights a rich interplay between recreational mathematics games and coding theory and encourages others to explore similar combinatorial games for hidden connections!