Gauss-Dickson Codes
Number Theory
2025-10-16 v1
Abstract
Let l be an odd prime. For primes, p \equiv 1 (mod l), Gauss (l = 3) and Dickson (l = 5) considered the Diophantine systems in terms of which cyclotomic numbers of order 3 and 5 were obtained. The aim of this paper is to show how to obtain 1-error detecting [2, 1, 2] code and 1-error correcting [4, 2, 3] code in terms of the solutions of these diophantine systems in the set up of finite fields of q = p^{\alpha} elements, p \equiv 1 (mod l), l = 3, 5
Cite
@article{arxiv.2510.13376,
title = {Gauss-Dickson Codes},
author = {Shashikant. A. Katre and Vikas S. Jadhav},
journal= {arXiv preprint arXiv:2510.13376},
year = {2025}
}
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13 Pages