Primitive idempotents and generator polynomials of some minimal cyclic codes of length pⁿq^m
by Pankaj Kumar; S.K. Arora; Sudhir Batra
International Journal of Information and Coding Theory (IJICOT), Vol. 2, No. 4, 2014

Abstract: Let p, q and l be distinct odd primes such that l is a primitive root modulo pⁿ 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 pⁿq^m over GF(l) are obtained. An algorithm is also given to factorise the polynomial (xⁿ - 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.

Online publication date: Tue, 02-Dec-2014

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