Abstract: It is proposed a modification of the algorithm Peterson-Gorenstein-Zierler on the based of Gauss method. To enhancing effectiveness this modification, i.e., to accelerate the detection and correction of errors in the non-binary Bose-Chaudhuri-Hocquenghem codes the technique is proposed. In the technique used computations apply tables of operations over an the elements finite field and instead of an elements is used an exponent of power from its representation in form power on the base primitive elements. The detailed description of decoding algorithm of received messages is given.