科研之友
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摘要
Z2(Z2 + uZ2)-additive cyclic codes were proved to be asymptotically good in 2020 by Yao et al., where u2 = 0. We extend the study to the double cyclic codes over two finite commutative chain rings. Let Rt = Zp[u]/(ut) = Zp + uZp + u2Zp + ... + ut-1Zp be a chain ring, where ut = 0. We construct a class of ZpRt-additive cyclic codes generated by pairs of polynomials, where p is a prime number. By using probabilistic methods, we study the asymptotic behaviour of the rates and relative minimum distances of a certain class of the codes. We show that there exists an asymptotically good infinite sequence of ZpRt-additive cyclic codes with the relative minimum distance of the code is convergent to delta, and the rate is convergent to 1 1+pt-1 for 0 < delta < 1 1+pt-1 , and t >= 1.
