A Class of Optimal Cyclic Codes With Two Zeros

Let m > 2 be an integer and p be an odd prime. We explore the minimum distance of p-ary cyclic codes of length n = 2(p
^m
- 1)/(p - 1) with two zeros. A sufficient condition for such cyclic codes with minimum distance at least three is obtained. A class of optimal p-ary cyclic codes with minimum distance four are presented. Four explicit constructions for such optimal cyclic codes are provided. The weight distribution of the dual of the cyclic code in the first construction is given.