An Algorithm for BCH Codes Extended with Finite State Automata

Issue title: Workshop on Combinatorial Algorithms

Article type: Research Article

Authors: Kelarev, Andrei

Affiliations: School of Information Technology and Mathematical Sciences University of Ballarat, P.O. Box 663, Ballarat, Victoria 3353, Australia. E-mail: [email protected]

Abstract: This article develops a combinatorial algorithm for a class of codes extending BCH codes and constructed with finite state automata. Our 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.

Keywords: finite fields, BCH codes, finite state automata

Journal: Fundamenta Informaticae, vol. 84, no. 1, pp. 51-60, 2008