Primitive idempotents and generator polynomials of some minimal cyclic codes of length p~nq~m

摘要

Let p, q and / be distinct odd primes such that / is a primitive root modulo p~n as well as modulo q~m with g.c.d. (φ(p),φ(q)) = 2. Then the explicit expressions for the complete set of 2mn + m + n + 1 primitive idempotents of the minimal cyclic codes of length p~nq~m over GF(l) are obtained. An algorithm is also given to factorise the polynomial (x~n - 1) over GF(k), where n is an integer such that g.c.d. (n, k) = 1. Using the algorithm generator polynomials of the above minimal cyclic codes can be computed numerically. Some bounds on the minimum distance of these minimal cyclic codes are also obtained.