Codes over subsets of algebras obtained by the Cayley-Dickson process

TL;DR

This paper introduces a new method for constructing binary block codes over subsets of Cayley-Dickson algebras, offering improved flexibility and code rates compared to existing techniques.

Contribution

It presents an algorithm that enhances code rate and flexibility for codes over Cayley-Dickson algebra subsets, surpassing previous methods.

Findings

The algorithm improves code rate over existing methods.

It provides greater flexibility in code construction.

Comparable to Lenstra's algorithm in elliptic curve cryptography.

Abstract

In this paper, we define binary block codes over subsets of real algebras obtained by the Cayley-Dickson process and we provide an algorithm to obtain codes with a better rate. This algorithm offers more flexibility than other methods known until now, similar to Lenstra algorithm on elliptic curves compared with Pollard algorithm.