I use Ubuntu, a Debian-based Linux operating system.
Install ImageMagick
sudo apt-get install imagemagick
Convert video to images.
avconv -i 00111.MTS 1%5d.png
Delete half of the images to speed up and decrease the size of the GIF.
rm *[13579].png
Convert the images to an animated GIF.
convert -loop 0 -resize 800 -layers optimize %d.png[100130-100300] awesome.gif