{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T04:58:59Z","timestamp":1769835539429,"version":"3.49.0"},"reference-count":18,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,14]],"date-time":"2022-12-14T00:00:00Z","timestamp":1670976000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universidad Pedag\u00f3gica y Tecnol\u00f3gica de Colombia","award":["SGI 3334"],"award-info":[{"award-number":["SGI 3334"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection, error correction, data transmission, and data storage. Codes are studied by various scientific disciplines, such as information theory, electrical engineering, mathematics, linguistics, and computer science, to design efficient and reliable data transmission methods. Many authors in the previous literature have discussed codes over finite fields, Gaussian integers, quaternion integers, etc. In this article, the author defines octonion integers, fundamental theorems related to octonion integers, encoding, and decoding of cyclic codes over the residue class of octonion integers with respect to the octonion Mannheim weight one. The comparison of primes, lengths, cardinality, dimension, and code rate with respect to Quaternion Integers and Octonion Integers will be discussed.<\/jats:p>","DOI":"10.3390\/computation10120219","type":"journal-article","created":{"date-parts":[[2022,12,15]],"date-time":"2022-12-15T02:20:57Z","timestamp":1671070857000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fundamental Results of Cyclic Codes over Octonion Integers and Their Decoding Algorithm"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0006-1156","authenticated-orcid":false,"given":"Muhammad","family":"Sajjad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan"}]},{"given":"Tariq","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5858-5011","authenticated-orcid":false,"given":"Robinson-Julian","family":"Serna","sequence":"additional","affiliation":[{"name":"Escuela de Matem\u00e1ticas y Estad\u00edstica, Universidad Pedag\u00f3gica y Tecnol\u00f3gica de Colombia, Avenida Central del Norte 39-115, Tunja 150003, Colombia"}]},{"given":"Zagalo Enrique","family":"Su\u00e1rez Aguilar","sequence":"additional","affiliation":[{"name":"Escuela de Matem\u00e1ticas y Estad\u00edstica, Universidad Pedag\u00f3gica y Tecnol\u00f3gica de Colombia, Avenida Central del Norte 39-115, Tunja 150003, Colombia"}]},{"given":"Omaida Sep\u00falveda","family":"Delgado","sequence":"additional","affiliation":[{"name":"Escuela de Matem\u00e1ticas y Estad\u00edstica, Universidad Pedag\u00f3gica y Tecnol\u00f3gica de Colombia, Avenida Central del Norte 39-115, Tunja 150003, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,14]]},"reference":[{"key":"ref_1","first-page":"241","article-title":"Parameterized codes over cycles","volume":"21","author":"Sarabia","year":"2013","journal-title":"An. 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Appl."},{"key":"ref_16","first-page":"1177","article-title":"Quaternion integers based higher length cyclic codes and their decoding algorithm","volume":"73","author":"Muhammad","year":"2022","journal-title":"Comput. Mater. Contin."},{"key":"ref_17","first-page":"1","article-title":"Designing Pair of Nonlinear Components of a Block Cipher Over Gaussian Integers","volume":"74","author":"Muhammad","year":"2022","journal-title":"Comput. Mater. Contin."},{"key":"ref_18","unstructured":"Giuliana, D., Peter, S., and Alian, V. (2003). Elementary Number Theory, Group Theory, and Ramanujan Graphs, Cambridge University Press."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/12\/219\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:41:26Z","timestamp":1760146886000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/12\/219"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,14]]},"references-count":18,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["computation10120219"],"URL":"https:\/\/doi.org\/10.3390\/computation10120219","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,14]]}}}