Logarithmic time encoding and decoding of integer error control codes

One of the most important characteristics of all error control codes (ECCs) is the complexity of the encoding/decoding algorithms. Today, there are many ECCs that can correct multiple bit errors, but at the price of high encoding/decoding complexity. Among the rare exceptions are integer ECCs (IECCs), whose serial encoding/decoding algorithms run in O(n) time, where n is the codeword length. In this article, we show that IECCs can be encoded/decoded even faster, that is, that their parallel encoding/decoding algorithms have O(log(2) n) time complexity.