What is a coaxial balun and what is its construction?
I'm not sure "coaxial balun" is really a standard term.

You can make a balun by wrapping coaxial cable around a magnetic core.  This is a common ham radio trick.  Depending on the application, you may be able to use a lossy core, like a simple iron rod or convenient bolt.  Only common mode currents will form a magnetic field.  Since you often want the balun to attenuate common mode signals from one side to the other, dissipating their energy in addition to having a high impedance to common mode signals can be useful.  Note that the two effects are different, and whether dissipation is desirable depends on the rest of the circuit and the overall purpose of the balun.