Abstract
We construct a class of ZprZps-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+ps−r2δ is greater than 12 and the relative distance of the code is convergent to δ, while the rate is convergent to 11+ps−r for 0<δ<11+ps−r and 1≤r<s. As a consequence, we prove that there exist numerous asymptotically good ZprZps-additive cyclic codes.
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