Aabstract：

A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani and Sochen. In our work closed formulae of the finite split oscillator dictionary are revisited by a simple proof, the structure of non-split tori of the group SL(2, F_p) is studied and an explicit algorithm for computing the finite non-split oscillator dictionary  is described.