Codes over a subset of Octonion Integers

TL;DR

This paper introduces a new class of error-correcting codes based on Octonion integers, demonstrating their ability to correct multiple errors with higher code rates than similar Quaternion-based codes.

Contribution

It defines codes over Octonion integers and proves their error correction capabilities and improved code rate compared to Quaternion-based codes.

Findings

Codes can correct up to two errors under certain conditions

Code rate exceeds that of Quaternion integer-based codes

Theoretical foundation for codes over Octonion integers

Abstract

In this paper we define codes over some Octonion integers. We prove that in some conditions these codes can correct up to two errors for a transmitted vector and the code rate of the codes is grater than the code rate of the codes defined on some subset of Quaternion integers.