1. A block code decoding method, comprising the steps of: (A) systematically encoding a first information code to generate a first block code comprising the first information code and a first parity check code; (B) transmitting the first block code; (C) receiving the first block code to be a first received block code comprising a first received information code corresponding to the first information code; (D) establishing a plurality of exclusive-or (XOR) mask vectors based on the dimension k being the length of the first information code and a selected Hamming distance of p, wherein the dimension of each of the plurality of XOR mask vectors is k, the plurality of XOR mask vectors are a combination of permuted mask vectors each having k components, wherein between 0 and p components in each mask vector have a value of i and a remaining components therein having a value of j, wherein each of i and j are binary values, each of the permuted mask vector corresponds to a permutation of the k components, and wherein the plurality of XOR mask vectors corresponds to all possible patterns of the first information code correctly and erroneously transmitted in the range of a Hamming distance less than p; (E) performing an XOR calculation with the first received information code and the plurality of XOR mask vectors and obtaining a plurality of k-bit second information codes; (F) encoding the plurality of second information codes and obtaining a plurality of second block codes; and (G) performing a correlation calculation with the first received code and the plurality of second block codes.