Asymptotically Good Additive Cyclic Codes Exist

Quasi-twisted codes of fixed index >1 have been shown recently to be asymptotically good (A. Alahmadi, C. Güneri, H. Shoaib, P. Solé, 2017). We use this result to construct asymptotically good additive constacyclic codes on any extension of a fixed degree of the base field. A similar result is proved for additive cyclic codes under Artin conjecture on primitive roots.