Asymptotically good [formula omitted]-additive cyclic codes.

We construct a class of Z p r Z p s -additive cyclic codes generated by pairs of polynomials, where p is a prime number. Based on probabilistic arguments, we determine the asymptotic rates and relative distances of this class of codes: the asymptotic Gilbert-Varshamov bound at 1 + p s − r 2 δ is greater than 1 2 and the relative distance of the code is convergent to δ , while the rate is convergent to 1 1 + p s − r for 0 < δ < 1 1 + p s − r and 1 ≤ r < s. As a consequence, we prove that there exist numerous asymptotically good Z p r Z p s -additive cyclic codes. [ABSTRACT FROM AUTHOR]