EvenQuads Game and Error-Correcting Codes
Name
42979_2025_Article_4293.pdf
Size
1.23 MB
Format
Adobe PDF
Checksum (MD5)
a243153bcdae9445da68da9fce401eec
Author(s)
Byrapuram, Nikhil
Choi, Hwiseo
Ge, Adam
Ge, Selena
Lee, Sylvia Z.
Liang, Evin
Mandal, Rajarshi
Oki, Aika
Wu, Daniel
Yang, Michael
Date Issued
August 22, 2025
Journal
SN Computer Science
Publisher
Springer Nature Singapore
Citation
Byrapuram, N., Choi, H., Ge, A. et al. EvenQuads Game and Error-Correcting Codes. SN COMPUT. SCI. 6, 763 (2025).
Version
Final published version
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. For any ℓ cards selected from the deck of EvenQuads, it is possible to construct an error-correcting linear binary code of length 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!
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s42979-025-04293-7
