Algebraic structure of additive conjucyclic codes over F4

In this paper, we are interested in finding an algebraic structure of conjucyclic codes of length n over the finite field F-4. We show that conjucyclic codes of length n over F-4 are related to binary cyclic codes of length 2n and show that there is a canonical bijective correspondence between the two sets. We illustrate how the factorization of the polynomial x(2n) + 1 plays a critical role in each setting. Moreover, we construct the generator and parity check matrices of conjucyclic codes of length n over F-4. (C) 2020 Elsevier Inc. All rights reserved.