Distance-optimality study for permutation codes using cyclic-shift prefix/suffix technique

Distance-preserving mappings is a technique that maps binary sequences to permutation sequences. Many mapping algorithms, which are called constructions have been introduced. Few constructions have been considered to be optimum on the sum of distances since they reached the upper bound on the sum of the Hamming distances for certain lengths of the permutation sequence. We introduce a technique based on the cyclic shift of a permutation symbol to understand the conditions that make any construction optimum.