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Keywords = octonion Mannheim distance

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12 pages, 756 KiB  
Article
Fundamental Results of Cyclic Codes over Octonion Integers and Their Decoding Algorithm
by Muhammad Sajjad, Tariq Shah, Robinson-Julian Serna, Zagalo Enrique Suárez Aguilar and Omaida Sepúlveda Delgado
Computation 2022, 10(12), 219; https://doi.org/10.3390/computation10120219 - 14 Dec 2022
Cited by 6 | Viewed by 1967
Abstract
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 [...] Read more.
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. Full article
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