{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:53:31Z","timestamp":1757624011994,"version":"3.44.0"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T00:00:00Z","timestamp":1755820800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T00:00:00Z","timestamp":1755820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100006919","name":"Massachusetts Institute of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100006919","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SN COMPUT. SCI."],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats: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 <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u2113<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> cards selected from the deck of EvenQuads, it is possible to construct an error-correcting linear binary code of length <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\ell$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u2113<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> 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!<\/jats:p>","DOI":"10.1007\/s42979-025-04293-7","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T15:40:18Z","timestamp":1755877218000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["EvenQuads Game and Error-Correcting Codes"],"prefix":"10.1007","volume":"6","author":[{"given":"Nikhil","family":"Byrapuram","sequence":"first","affiliation":[]},{"given":"Hwiseo","family":"Choi","sequence":"additional","affiliation":[]},{"given":"Adam","family":"Ge","sequence":"additional","affiliation":[]},{"given":"Selena","family":"Ge","sequence":"additional","affiliation":[]},{"given":"Sylvia Zia","family":"Lee","sequence":"additional","affiliation":[]},{"given":"Evin","family":"Liang","sequence":"additional","affiliation":[]},{"given":"Rajarshi","family":"Mandal","sequence":"additional","affiliation":[]},{"given":"Aika","family":"Oki","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Yang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0868-8981","authenticated-orcid":false,"given":"Tanya","family":"Khovanova","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"4293_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/b97662","volume-title":"Linear algebra done right","author":"S Axler","year":"1997","unstructured":"Axler S. Linear algebra done right. Springer; 1997."},{"issue":"5","key":"4293_CR2","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1109\/PROC.1980.11696","volume":"68","author":"ER Berlekamp","year":"1980","unstructured":"Berlekamp ER. The technology of error-correcting codes. Proc IEEE. 1980;68(5):564\u201393.","journal-title":"Proc IEEE"},{"issue":"2","key":"4293_CR3","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/0097-3165(84)90006-2","volume":"36","author":"TC Brown","year":"1984","unstructured":"Brown TC, Buhler JP. Lines imply spaces in density Ramsey theory. J Combin Theory Ser A. 1984;36(2):214\u201320.","journal-title":"J Combin Theory Ser A"},{"key":"4293_CR4","unstructured":"Byrapuram N, Choi H, Ge A, Ge S, Khovanova T, Lee SZ, Liang E, Mandal R, Oki A, Wu D, Yang M. Card games unveiled: exploring the underlying linear algebra; 2023. math.HO. arXiv:2306.09280."},{"key":"4293_CR5","unstructured":"Byrapuram N, Choi H, Ge A, Ge S, Khovanova T, Lee SZ, Liang E, Mandal R, Oki A, Wu D, Yang M. QuadSquares; 2023. math.HO and math.CO. arXiv:2308.07455."},{"key":"4293_CR6","volume-title":"Fundamentals of error-correcting codes","author":"W Cary Huffman","year":"2010","unstructured":"Cary Huffman W, Pless V. Fundamentals of error-correcting codes. Cambridge University Press; 2010."},{"issue":"13","key":"4293_CR7","first-page":"71","volume":"7","author":"E Chen","year":"2020","unstructured":"Chen E, Du W, Gupta T, Khovanova T, Li A, Mallajosyula S, Raghavan R, Sinha A, Smith M, Qian M, Wang S. The classification of magic SET squares. Recreat Math Mag. 2020;7(13):71\u201394.","journal-title":"Recreat Math Mag"},{"key":"4293_CR8","volume-title":"Sphere packings, lattices and groups","author":"JH Conway","year":"2013","unstructured":"Conway JH, Sloane NJA. Sphere packings, lattices and groups, vol. 290. Springer; 2013."},{"key":"4293_CR9","doi-asserted-by":"crossref","unstructured":"Crager J, Flores F, Goldberg TE, Rose LL, Rose-Levine D, Thornburgh D, Walker R. How many cards should you lay out in a game of EvenQuads? A study of 2-caps in $$AG(2, n)$$; 2022. math.CO. arXiv:2212.05353.","DOI":"10.1007\/s44007-023-00047-0"},{"key":"4293_CR10","volume-title":"The joy of SET: the many mathematical dimensions of a seemingly simple card game","author":"G Gordon","year":"2017","unstructured":"Gordon G, Gordon H, Gordon R, McMahon L. The joy of SET: the many mathematical dimensions of a seemingly simple card game. Princeton University Press; 2017."},{"key":"4293_CR11","doi-asserted-by":"crossref","unstructured":"Gordon G, McMahon E. Error detection and correction using SET\u00ae. In: The mathematics of various entertaining subjects research in recreational mathematics, vol. 14; 2016. p. 199\u201312.","DOI":"10.1515\/9781400881338-016"},{"issue":"2","key":"4293_CR12","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1002\/j.1538-7305.1950.tb00463.x","volume":"29","author":"RW Hamming","year":"1950","unstructured":"Hamming RW. Error detecting and error correcting codes. Bell Syst Tech J. 1950;29(2):147\u201360.","journal-title":"Bell Syst Tech J"},{"key":"4293_CR13","unstructured":"Rose LL. Quads: a SET-like game with a Twist. http:\/\/sigmaa.maa.org\/mcst\/QUADS%20-%20SET%20WITH%20A%20TWIST.pdf"},{"key":"4293_CR14","unstructured":"OEIS Foundation Inc. The on-line encyclopedia of integer sequences; 2023. https:\/\/oeis.org."},{"key":"4293_CR15","unstructured":"Vinci J. The maximum number of sets for N cards and the total number of internal sets for all partitions of the deck; 2022. https:\/\/www.setgame.com\/sites\/default\/files\/teacherscorner\/SETPROOF.pdf."}],"container-title":["SN Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-025-04293-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42979-025-04293-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42979-025-04293-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T10:44:30Z","timestamp":1757414670000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42979-025-04293-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,22]]},"references-count":15,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["4293"],"URL":"https:\/\/doi.org\/10.1007\/s42979-025-04293-7","relation":{},"ISSN":["2661-8907"],"issn-type":[{"type":"electronic","value":"2661-8907"}],"subject":[],"published":{"date-parts":[[2025,8,22]]},"assertion":[{"value":"24 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 August 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Moreover, Research Involving Human and\/or Animals is not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}],"article-number":"763"}}