(n, n(n − 1), n − 1) Permutation codes based on packing and Mendelsohn designs

摘要

Mendelsohn design was first used to construct n - 1 blocks of one optimal 2-(n, n, 2) packing which is isomorphic to an (n, n - 1, n - 1) permutation array. The n-ary shift register (SR) formed by a group of k binary SRs of length n was constructed and then used to operate n - 1 blocks of the 2-(n, n, 2) packing which can generate n(n - 1) blocks of another optimal 2-(n, n, 2n) packing from which a family of (n, n(n - 1), n - 1) permutation codes can be constructed.