Algebraic structure of F_q-linear conjucyclic codes over finite field F_{q^2}

Abstract

Recently, Abualrub et al. illustrated the algebraic structure of additive conjucyclic codes over F_4 (Finite Fields Appl. 65 (2020) 101678). In this paper, our main objective is to generalize their theory. Via an isomorphic map, we give a canonical bijective correspondence between F_q-linear additive conjucyclic codes of length n over F_{q^2} and q-ary linear cyclic codes of length 2n. By defining the alternating inner product, our proposed isomorphic map preserving the orthogonality can also be proved. From the factorization of the polynomial x^{2n}-1 over F_q, the enumeration of F_{q}-linear additive conjucyclic codes of length n over F_{q^2} will be obtained. Moreover, we provide the generator and parity-check matrices of these q^2-ary additive conjucyclic codes of length n