On ZprZpsZpt-additive cyclic codes exhibit asymptotically good properties.

In this paper, we construct a class of Z p r Z p s Z p t -additive cyclic codes generated by 3-tuples of polynomials, where p is a prime number and 1 ≤ r ≤ s ≤ t . We investigate the algebraic structure of these codes and establish that it is possible to determine generator matrices for a subfamily of codes within this class. We employ a probabilistic approach to analyze the asymptotic properties of these codes. For any positive real number δ satisfying 0 < δ < 1 such that the asymptotic Gilbert-Varshamov bound at k + l + n 3 p r - 1 δ is greater than 1 2 , we demonstrate that the relative distance of the random code converges to δ , while the rate of the random code converges to 1 k + l + n . Finally, we conclude that the Z p r Z p s Z p t -additive cyclic codes exhibit asymptotically good properties. [ABSTRACT FROM AUTHOR]