Encoding through generalized polynomial codes

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

An algorithm for BCH codes extended with finite state automata

This articles develops a combinatorial algorithm for a class of codes extending BCH codes and constructed with finite state automata. Ou algorithm computes the largest number of errors that the extended codes can correct, and finds a generator for each optimal code in this class of extensions. The question of finding codes with largest possible information rates remains open.C