Constructions of cyclic codes and extended primitive cyclic codes with their applications

Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear based on special polynomials over finite fields. The first family are extended primitive cyclic which affine-invariant. second reducible codes. parameters these their duals determined. As the application, prove that hold t-designs, where t=2,3. minimum localities also determined optimal locally recoverable derived.