Fundamental Results of Cyclic Codes over Octonion Integers and Their Decoding Algorithm

Coding theory is the study of properties codes and their respective fitness for specific applications. Codes are used data compression, cryptography, error detection, correction, transmission, storage. studied by various scientific disciplines, such as information theory, electrical engineering, mathematics, linguistics, computer science, to design efficient reliable transmission methods. Many authors in previous literature have discussed over finite fields, Gaussian integers, quaternion etc. In this article, author defines octonion fundamental theorems related encoding, decoding cyclic residue class integers with respect Mannheim weight one. The comparison primes, lengths, cardinality, dimension, code rate Quaternion Integers Octonion will be discussed.