Name
Abstract | ||
|---|---|---|
In this paper, we define and study \emph{quantum cyclic codes}, a
generalisation of cyclic codes to the quantum setting. Previously studied
examples of quantum cyclic codes were all quantum codes obtained from classical
cyclic codes via the CSS construction. However, the codes that we study are
much more general. In particular, we construct cyclic stabiliser codes with
parameters $[[5,1,3]]$, $[[17,1,7]]$ and $[[17,9,3]]$, all of which are
\emph{not} CSS. The $[[5,1,3]]$ code is the well known Laflamme code and to the
best of our knowledge the other two are new examples. Our definition of
cyclicity applies to non-stabiliser codes as well; in fact we show that the
$((5,6,2))$ nonstabiliser first constructed by Rains\etal~
cite{rains97nonadditive} and latter by Arvind
\etal~\cite{arvind:2004:nonstabilizer} is cyclic. We also study stabiliser
codes of length $4^m +1$ over $\mathbb{F}_2$ for which we define a notation of
BCH distance. Much like the Berlekamp decoding algorithm for classical BCH
codes, we give efficient quantum algorithms to correct up to
$\floor{\frac{d-1}{2}}$ errors when the BCH distance is $d$. |
Year | Venue | Keywords |
|---|---|---|
2010 | Clinical Orthopaedics and Related Research | information theory,bch code,quantum algorithm,cyclic code |
Field | DocType | Volume |
Discrete mathematics,Quantum,Quantum codes,Notation,Combinatorics,Generalization,Cyclic code,BCH code,Quantum algorithm,Decoding methods,Mathematics | Journal | abs/1007.1 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sagarmoy Dutta | 1 | 0 | 1.01 |
| Piyush P. Kurur | 2 | 88 | 9.41 |