The separation of binary relative three-weight codes and its applications

摘要

The separation and its applications of binary relative three-weight codes are studied. We first present a certain formula for computing the minimum values of the cardinality of separating coordinate position (CSCP) of some codeword sets for any binary linear code, and then with the above formula, we calculate all the minimum values of the CSCP of binary relative three-weight codes so as to determine their separation. By using the obtained separation of binary relative three-weight codes, some new binary separating codes are constructed. Based on a family of the minimum values of the CSCP of binary relative three-weight codes, we also determine all the minimal codewords and the trellis complexity of binary relative three-weight codes.