RFID coil antenna

N&R is a leading supplier of smart cards and RFDI tags for global system integrators and distributors. We offer a wide range of RFID tags with contact chip or contactless chip (LF, HF, UHF) ,such as ISO CR80 card, wristband, key fob, disc tag, laundry tag, tire tag ect. They are widely applied in different kinds of applications. For examples: access control, smart payment, loyalty system, assets tracking, identifications, time and attendance management.
Basically I am motivated to replace the antenna on this RFID reader. The reader is really cheap, and fits my porpoise, its recognized as a USB keyboard.

My Idea is to build a new antenna that can be fitted into a PVC tube and have a usb "reading rod". Basically I want to make a new coil with copper cable which area is a rectangle instead of a square.

Hackaday has provided me with some information about this, but nothing useful about antenna modding.

Thanks a friend (Chris) I manage to get some technical documents about this matter, some turned to be really useful and cover basic subject (like Magnetism, Faraday's Law, Mutual induction) it really help me understand more about RFID, it sure brought me memories when I was in college, but could not find any decisive information on how to shape a new antenna.

I know antenna shapes and geometry are dependent on: Frequency (125 Khz in this case) and range of reading (of the tags) and number of turns. Of course many other items, but they are purely derivative from the two I mentioned first.
Priority 1 Design carry a stock of these RFID coil antennas. Our RFID coil antennas have been designed by us
specifically for our RFID readers and transponders but can easily be used by hobbyists and professionals to
create their own RFID designs.
This coil was designed to give our rfid readers longer read range.
Typical read distances based on our example circuit are 8cm for keytags
and 10cm for rfid cards.
A 10cm coil allows for a larger field pattern and slightly larger read ranges over our 49mm antennas. especially when larger tags are being read.
This coil was created for our RFIDLOG series of rfid data loggers. Its large 16cm diameter allows for greater read range than a smaller antenna will allow.
Its also suitable for use with our RFIDRW-E series of readers with only
a slight addition to the tuning capacitor.
coil allows for a larger field pattern and longer read ranges. When connected to out RFIDRW-E-232E enhanced reader this antenna allows typical read ranges of 27cm for a 32mm FDXB disc tag.
RFID reader anntena coil, the actual read range for  reader is about 4cm. I plan to remove the original anntena coil and replace with another anntena coil to improve the reading range. so, what type of material i needed to build the antenna coil? for example copper? is that correct? how many turn for the anntena coil? how many diameter for the anntena coil

http://www.nfcandrfid.com/products_info/ISO15693-RFID-coil-antenna-315101.html