Gauss-Dickson Codes
Abstract
Let l be an odd prime. For primes, p 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 = pα elements, p 1 (mod l), l = 3, 5
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