The Direct Sum Construction Of Two-weight Cyclic Codes

In this paper, we discuss a class of two-weight reducible cyclic codes, which can be constructed as the direct sum of two one-weight simplex codes. For those two-weight reducible cyclic codes, by means of the conclusions and properties of character and Gaussian sum, we get their two nonzero weights, and we give a criterion to check that whether those two-weight reducible cyclic codes are projective.