ℤpℤps-additive cyclic codes are asymptotically good

We construct a class of ℤ p ℤ p s -additive cyclic codes generated by pairs of polynomials, where p is a prime number. The generator matrix of this class of codes is obtained. By establishing the relationship between the random ℤ p ℤ p s -additive cyclic code and random quasi-cyclic code of index 2 over ℤ p , the asymptotic properties of the rates and relative distances of this class of codes are studied. As a consequence, we prove that ℤ p ℤ p s -additive cyclic codes are asymptotically good since the asymptotic GV-bound at 1 + p s − 1 2 δ is greater than 1 2 , the relative distance of the code is convergent to δ , while the rate is convergent to 1 1 + p s − 1 for 0 < δ < 1 1 + p s − 1 .