EvenQuads Game and Error-Correcting Codes
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 cards from the deck of EvenQuads, we can build an error-correcting linear binary code of length 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.
Cite
@article{arxiv.2310.01257,
title = {EvenQuads Game and Error-Correcting Codes},
author = {Nikhil Byrapuram and Hwiseo and Choi and Adam Ge and Selena Ge and Tanya Khovanova and Sylvia Zia Lee and Evin Liang and Rajarshi Mandal and Aika Oki and Daniel Wu and Michael Yang},
journal= {arXiv preprint arXiv:2310.01257},
year = {2023}
}
Comments
20 pages, 8 tables