Construction method for (n,n(n-1),n-1) permutation group code based on coset partition and codebook generator thereof

Abstract

A construction method for a (n,n(n−1),n−1) permutation group code based on coset partition is provided. The presented (n,n(n−1),n−1) permutation group code has an error-correcting capability of d−1 and features a strong anti-interference capability for channel interferences comprising multi-frequency interferences and signal fading. As n is a prime, for a permutation code family with a minimum distance of n−1 and a code set size of n(n−1), the invention provides a method of calculating n−1 orbit leader permutation codewords by O={αo}(mod n) and enumerating residual codewords of the code set by P=CO={(l)O}={(r)O)}. Besides, a generator of the code set thereof is provided. The (n,n(n−1),n−1) permutation group code of the invention is an algebraic-structured code, n−1 codewords of the orbit leader array can be obtained simply by adder and (mod n) calculator rather than multiplication of positive integers. Composition operations of the cyclic subgroup Cacting on all permutations oof the orbit leader permutation array Oare replaced by well-defined cyclic shift composite operation functions (l)and (r)so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.