FROM SKEW-CYCLIC CODES TO ASYMMETRIC QUANTUM CODES
We introduce an additive but not F-4-linear map S from F-4(n) to F-4(2n) 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, 2(2k), 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 theta-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.
skew-cyclic codes quantum codes cyclic codes additive codes best-known linear codes reed-solomon codes self-orthogonal codes