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

The objective of this letter is to construct two classes of cyclic codes over <inline-formula> <tex-math notation="LaTeX">$F_{p}$ </tex-math></inline-formula> with few weights, where <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> 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.

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