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

摘要

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_n={αo₁}_α=1^n-1(mod n) and enumerating residual codewords of the code set by P_n=C_nO_n={(l₁)^n-1O_n}={(r_n)^n-1O_n}. 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 C_n acting on all permutations o_α of the orbit leader permutation array O_n are replaced by well-defined cyclic shift composite operation functions (l₁)^n-1 and (r_n)^n-1 so that the action of the cyclic group acting on permutations is realized by a group of cyclic shift registers.