A family of cyclic codes with two zeros

Cyclic codes have been applied in communication systems, data storage systems and consumer electronics widely. In this work, we explore q-ary cyclic codes of length n = q(m-1) /r having two zeros. For such cyclic codes, a sufficient and necessary condition with minimum distance two is given. It is shown that such cyclic codes have minimum distance at most three when q > 2r + 1. For r = q-1 / 2, we obtain an optimal family of cyclic codes with parameters [ 2(q(m)-1) /q-1, 2(q(m)- 1)/ q-1 - 2m, 4].