@article{article_525606, title={Some results on free Euclidean self-dual codes over F2+vF2}, journal={Sakarya University Journal of Science}, volume={23}, pages={1131–1136}, year={2019}, DOI={10.16984/saufenbilder.525606}, url={https://izlik.org/JA43MP26WJ}, author={Aksoy, Refia and Çalışkan, Fatma}, keywords={Euclidean self-dual codes,codes over rings,Chinese remainder theorem}, abstract={<p class="MsoNormal"> <span lang="en-us" xml:lang="en-us"> In this
paper, free Euclidean self-dual codes over the ring  F <sub>2 </sub> </span> <span lang="en-us" xml:lang="en-us"> + v F <sub>2  </sub> </span> <span lang="en-us" xml:lang="en-us">with v <sup>2 </sup> =v </span> <span style="font-size:12pt;font-family:’Times New Roman’, serif;"> </span> <span lang="en-us" xml:lang="en-us"> of order 4 are considered. A necessary and
sufficient condition for the form of the generator matrix of a free Euclidean
self-dual code is given. By using the distance preserving Gray map from  </span> <span lang="en-us" style="font-size:12.6px;" xml:lang="en-us"> F <sub style="font-size:9.45px;">2 </sub> </span> <span lang="en-us" style="font-size:12.6px;" xml:lang="en-us"> + v F <sub style="font-size:9.45px;">2 </sub> </span> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us">  </span> <span style="font-size:12pt;font-family:’Times New Roman’, serif;"> </span> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us"> to F <sub>2 </sub> x </span> <span style="font-size:12pt;font-family:’Times New Roman’, serif;">  </span> <span style="font-size:11.34px;"> F </span> <sub style="font-size:8.505px;">2 </sub> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us">,
the generator matrix of the binary code which corresponds the code over the
ring  </span> <span lang="en-us" style="font-size:12.6px;" xml:lang="en-us">F <sub style="font-size:9.45px;">2 </sub> </span> <span lang="en-us" style="font-size:12.6px;" xml:lang="en-us"> + v F <sub style="font-size:9.45px;">2 </sub> </span> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us">  </span> <span style="font-size:12pt;font-family:’Times New Roman’, serif;"> </span> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us"> is obtained. The codes of lengths up to 100 over
the ring  </span> <span lang="en-us" style="font-size:12.6px;" xml:lang="en-us">F <sub style="font-size:9.45px;">2 </sub> </span> <span lang="en-us" style="font-size:12.6px;" xml:lang="en-us"> + v F <sub style="font-size:9.45px;">2 </sub> </span> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us">  </span> <span style="font-size:12pt;font-family:’Times New Roman’, serif;"> </span> <span lang="en-us" style="font-size:.9em;" xml:lang="en-us">are
found. </span> </p>}, number={6}