Abstract: In this paper, symmetry binary tree coder （STQM） and optimal binary tree coder （OTQM） are proposed based on the QM\|coder. STQM and OTQM are multiplication\|free arithmetic coders with high performance for multi\|symbol alphabet, which not only keep the encoding efficiency of QM\|coder, but also keep its high speed. OTQM can adjust its binary tree structure dynamically. This advantage enables the encoder to reach its maximum speed. STQM can be implemented by special hardware as a parallel coder, so that it is very useful for video coding.