Asymptotically good Z_p~rZ_p~s-additive cyclic codes

摘要

We construct a class of Z(pr) Z(ps)-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 delta is greater than 1/2 and the relative distance of the code is convergent to delta, while the rate is convergent to 1/1+p(s-r) for 0 delta 1/1+p(s-r) and 1 = r s. As a consequence, we prove that there exist numerous asymptotically good Z(pr) Z(ps)-additive cyclic codes. (C) 2020 Elsevier Inc. All rights reserved.