We introduce an additive but not F4​-linear map S from
F4n​ to F42n​ and exhibit some of its interesting
structural properties. If C is a linear [n,k,d]4​-code, then S(C) is an
additive (2n,22k,2d)4​-code. If C is an additive cyclic code then S(C)
is an additive quasi-cyclic code of index 2. Moreover, if C is a module
θ-cyclic code, a recently introduced type of code which will be
explained below, then S(C) is equivalent to an additive cyclic code if n is
odd and to an additive quasi-cyclic code of index 2 if n is even. Given any
(n,M,d)4​-code C, the code S(C) is self-orthogonal under the trace
Hermitian inner product. Since the mapping S preserves nestedness, it can be
used as a tool in constructing additive asymmetric quantum codes.Comment: 16 pages, 3 tables, submitted to Advances in Mathematics of
Communication