On the Decoding Complexity of Cyclic Codes Up to the BCH Bound

—The standard algebraic decoding algorithm of cyclic codes [n, k, d] up to the BCH bound t is very efficient and practical for relatively small n while it becomes unpractical for large n as its computational complexity is O(nt). Aim of this paper is to show how to make this algebraic decoding computationally more efficient: in the case of binary codes, for example, the complexity of the syndrome computation drops from O(nt) to O(t √ n), and that of the error location from O(nt) to at most max{O(t √ n), O(t2 log(t) log(n))}.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Davide Schipani, Michele Elia, Joachim Rosenthal
• Keywords: Algebraic Decoding Algorithm, Computational Complexity, CORR 2011, Cyclic Codes, Education