The Weight Distributions of Two Classes of Nonbinary Cyclic Codes With Few Weights

摘要

The objective of this letter is to construct two classes of cyclic codes over $F_{p}$ with few weights, where $p$ is an odd prime. The weight distributions of these codes are determined. Some of the cyclic codes are optimal, which refers to meeting a certain bound on linear codes. The number of nonzero weights of these codes is not more than five and these codes can be employed to obtain secret sharing schemes.