{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:12:07Z","timestamp":1760058727285,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T00:00:00Z","timestamp":1745625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Cross parity codes are mostly used as 2-dimensional codes, and sometimes as 3-dimensional codes. We argue that higher dimensions can help to reduce the number of parity bits, and thus deserve further investigation. As a start, we investigate parities from (d\u22122)-dimensional hyperplanes in d-dimensional parity codes, instead of parities from (d\u22121)-dimensional hyperplanes as usual.<\/jats:p>","DOI":"10.3390\/computers14050161","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T05:21:31Z","timestamp":1745817691000},"page":"161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["High-Dimensional Cross Parity Codes and Parities from Lower Than (d \u2212 1)-Dimensional Hyperplanes"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0303-6140","authenticated-orcid":false,"given":"J\u00f6rg","family":"Keller","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, FernUniversit\u00e4t in Hagen, 58084 Hagen, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1145\/366853.366878","article-title":"n-dimensional codes for detecting and correcting multiple errors","volume":"4","author":"Rubinoff","year":"1961","journal-title":"Commun. ACM"},{"key":"ref_2","unstructured":"Wong, T.F., and Shea, J.M. (2001, January 24\u201329). Multi-dimensional parity-check codes for bursty channels. Proceedings of the 2001 IEEE International Symposium on Information Theory, Washington, DC, USA."},{"key":"ref_3","first-page":"94","article-title":"Modified Cross Parity Codes for Adjacent Double Error Correction","volume":"Volume 13949","author":"Goumas","year":"2023","journal-title":"Proceedings of the Architecture of Computing Systems\u201436th International Conference, ARCS 2023"},{"key":"ref_4","unstructured":"Lin, S., and Costello, D.J. (1983). Error Control Coding\u2014Fundamentals and Applications, Prentice Hall."},{"key":"ref_5","unstructured":"Gizopoulos, D., Alexandrescu, D., Papavramidou, P., and Maniatakos, M. (2019, January 1\u20133). A New DEC\/TED Code for Fast Correction of 2-Bit-Errors. 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Proceedings of the 2019 International Conference on Applied Electronics (AE), Pilsen, Czech Republic.","DOI":"10.23919\/AE.2019.8867037"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Tomlinson, M., Tjjai, C.J., Ambroze, M.A., Ahmed, M., and Jibril, M. (2017). Error-Correction Coding and Decoding, Springer.","DOI":"10.1007\/978-3-319-51103-0"}],"container-title":["Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/5\/161\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:22:13Z","timestamp":1760030533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-431X\/14\/5\/161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,26]]},"references-count":9,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["computers14050161"],"URL":"https:\/\/doi.org\/10.3390\/computers14050161","relation":{},"ISSN":["2073-431X"],"issn-type":[{"type":"electronic","value":"2073-431X"}],"subject":[],"published":{"date-parts":[[2025,4,26]]}}}