This paper introduces novel constructions of cyclic codes using semigroup rings instead of polynomial rings. These constructions are applied to define and investigate the BCH, alternant, Goppa, and Srivastava codes. This makes it possible to improve several recent results due to Andrade and Palazzo [1]. © 2011 SBMAC.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)