A class of ZprZpsZpt-additive cyclic codes that are formed by 3-tuples of polynomials are constructed in this paper,where p is a prime number and 1 ≤ r ≤ s ≤t.Having established a connection between the random ZprZpsZpt-additive cyclic codes and the quasi-abelian complementary dual codes of index 3,we construct a family of codes of increasing length whose relative minimum distances converge δ while their rates converge 1/3,for 0＜δ＜3/2(1+ps-r+pt-r).Consequently,we demonstrate that a large number of ZprZpsZpt-additive cyclic codes are asymptotically good.
ZprZpsZpt-additive cyclic codesrandom codesmodule-isomorphismrelative distanceasymptotically good codes
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