Abstract The decoding speed is the biggest problem of random codes based on quasigroups proposed elsewhere. These codes are a combination of cryptographic algorithms and error-correcting codes. In our previous paper we proposed Cut-Decoding algorithm which is 4.5 times faster than the original one for code (72,288). In this paper, four new modifications (so-called 4-Sets-Cut-Decoding algorithms) of this algorithm are proposed in order to obtain an improvement of the decoding speed. We present and analyze several experimental results obtained with different algorithms for random codes based on quasigroups. It is shown that using new algorithms, improvement of the efficiency and decoding speed is obtained. Also, we derive the upper bound for packet-error probability obtained with Cut-Decoding and 4-Sets-Cut-Decoding algorithm. At the end, some methods for reducing the number of unsuccessful decodings in the new proposed algorithms are considered.