Computer Science – Information Theory
Scientific paper
2010-05-06
Computer Science
Information Theory
16 pages, 3 tables, submitted to Advances in Mathematics of Communications
Scientific paper
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.
Ezerman Martianus Frederic
Ling San
Sole Patrick
Yemen Olfa
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