Dipole Antenna

I think you're mixing a few terms. In a strict sense the transmitter is the active electronics while an antenna is where wire based signals meets free-space based signals. But that's just my loose definition. But one can and many people have used a dipole antenna for a 10Mhz signal. You are correct though that the half wavelength dimension at this frequency means 15 meters of dipole often gets unwieldy. A nice antenna basics site and an over all DX radio site for you to peruse.

a half wave dipole at 10 meters would be 15 meters overall, with a center feed.

http://en.wikipedia.org/wiki/Dipole_antenna

The length varies. You can also make a vertical on a ground plane. These can be 1/4 wave, 3/8 wave etc

http://www.google.ca/#hl=en&safe=off&q=vertical+%2Bantenna&meta=&aq=f&oq=vertical+%2Bantenna&fp=2c632e1fcd336022

If there is a need to save space, you can insert a loading coil at the base or elsewhere that has the effect of making the antenna shorter, but it still resonates as if it was full length. This is often used in rotary yagi or beam antenna, and also on vertical antennas

http://www.google.ca/#hl=en&safe=off&q=%22loading+coil%22+%2Bantenna&meta=&aq=&oq=%22loading+coil%22+%2Bantenna&fp=2c632e1fcd336022

If size is an issue, you could use a helix antenna. This type of antenna is often used by amateur radio enthusiasts for mobile applications in the HF frequency band. There is a lot of stuff on the internet, here is one link which may be useful:

http://www.dxzone.com/cgi-bin/dir/jump2.cgi?ID=11153

Why are you guys doing this kid's homework for him? You can make a dipole by merging a maniac depressive with an anxiety disorder....hold on... that's how to make a bi-polar...

What is too long for your application? How much area do you have to put up an antenna? Do you have any height limits? How far away is your intended receive station? How much rf power will you be transmitting? How far away from the actual antenna will the transmitter be? There are many antenna designs you could use but what are your limitations? Your answers to the above questions will help us give you your best options.