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arXiv · 2310.01257

EvenQuads Game and Error-Correcting Codes

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

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. Given $\ell$ cards from the deck of EvenQuads, we can build an error-correcting linear binary code of length $\ell$ and Hamming distance 4. The quads correspond to codewords of weight 4. Error-correcting codes help us calculate the possible number of quads when given 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.

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Nikhil Byrapuram, Hwiseo, Choi, Adam Ge, Selena Ge, Tanya Khovanova, Sylvia Zia Lee, Evin Liang, Rajarshi Mandal, Aika Oki, Daniel Wu, Michael Yang. 2023-10-02. EvenQuads Game and Error-Correcting Codes. https://arxiv.org/abs/2310.01257

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