From skew-cyclic codes to asymmetric quantum codes
Ezerman, Martianus Frederic
Date of Issue2011
School of Physical and Mathematical Sciences
We introduce an additive but not F4-linear map S from Fn4 To F24n 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.
Advances in mathematics of communications
©2011 The American Institute of Mathematical Sciences (AIMS) This paper was published in Advances in Mathematics of Communications and is made available as an electronic reprint (preprint) with permission of The American Institute of Mathematical Sciences AIMS.The paper can be found at http://dx.doi.org/10.3934/amc.2011.5.41. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.