713 research outputs found
Non-Additive Quantum Codes from Goethals and Preparata Codes
We extend the stabilizer formalism to a class of non-additive quantum codes
which are constructed from non-linear classical codes. As an example, we
present infinite families of non-additive codes which are derived from Goethals
and Preparata codes.Comment: submitted to the 2008 IEEE Information Theory Workshop (ITW 2008
Non-Additive Quantum Codes from Goethals and Preparata Codes
We extend the stabilizer formalism to a class of non-additive quantum codes
which are constructed from non-linear classical codes. As an example, we
present infinite families of non-additive codes which are derived from Goethals
and Preparata codes.Comment: submitted to the 2008 IEEE Information Theory Workshop (ITW 2008
New characterisations of the Nordstrom–Robinson codes
In his doctoral thesis, Snover proved that any binary code
is equivalent to the Nordstrom-Robinson code or the punctured
Nordstrom-Robinson code for or respectively. We
prove that these codes are also characterised as \emph{completely regular}
binary codes with or , and moreover, that they are
\emph{completely transitive}. Also, it is known that completely transitive
codes are necessarily completely regular, but whether the converse holds has up
to now been an open question. We answer this by proving that certain completely
regular codes are not completely transitive, namely, the (Punctured) Preparata
codes other than the (Punctured) Nordstrom-Robinson code
Problems on q-Analogs in Coding Theory
The interest in -analogs of codes and designs has been increased in the
last few years as a consequence of their new application in error-correction
for random network coding. There are many interesting theoretical, algebraic,
and combinatorial coding problems concerning these q-analogs which remained
unsolved. The first goal of this paper is to make a short summary of the large
amount of research which was done in the area mainly in the last few years and
to provide most of the relevant references. The second goal of this paper is to
present one hundred open questions and problems for future research, whose
solution will advance the knowledge in this area. The third goal of this paper
is to present and start some directions in solving some of these problems.Comment: arXiv admin note: text overlap with arXiv:0805.3528 by other author
- …