A CLASS OF THREE-WEIGHT CYCLIC CODES

In this paper, the value distribution of the exponential sum $S\left( {\alpha, \beta } \right) = \sum\limits_{x \in {\mathbb{ F }_p}m} \chi \left( {\alpha {x^{\frac{{{p^k} + 1}}{2}}} + \beta {x^{\frac{{{p^{3k}} + 1}}{2}}}} \right) $ is investigated. Applying the value distribution of S ( α , β ), the weight distribution of a class of p -ary cyclic codes is determined. It turns out that the proposed cyclic codes has three nonzero weights, here p is an odd prime, m and k are two positive integers such that m /gcd( m , k ) is odd, k =/gcd( m , k ) is even and m ≥ 3.