Random Codes Based on Quasigroups (RCBQ) are cryptcodes that provide a correction of transmission errors and an information security, all with one algorithm. Standard algorithm, Cut-Decoding and 4-Sets-Cut-Decoding algorithms are different versions of RCBQ and they are proposed elsewhere. The decoding in all these algorithms is list decoding, so the speed of the decoding depends on the list size. In order to decrease the list size, Fast-Cut-Decoding and Fast-4-Sets-Cut-Decoding algorithms are proposed elsewhere and they improve performances of these codes for transmission through a Gaussian channel. Here, we propose a new modification of these algorithms to improve their properties for transmission through a burst channels.