Abstract
Let Fq be a finite field with q elements and n=l1m1l2m2, m1≥1, m2≥1, where l1, l2 are distinct primes and l1l2|q−1. In this paper, we give all irreducible factors of xl1m1l2m2−1 over Fq and all primitive idempotents in a ring Fq[x]/〈xl1m1l2m2−1〉. Furthermore, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length l1m1l2m2 over Fq.
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