Iterated codes with improved performance (Corresp.)

Improvements on the rates of iterated codes for error-free decoding on the binary symmetric channel are presented. Approximations to the performance of Elias's original error-free codes are replaced with virtually exact results that demonstrate higher code rates and the ability to decode from noisier channels than the original results indicated. Prefacing an Elias code with iterations of one or more primitive Bose-Chaudhuri-Hoequenghem (BCH) codes is shown to provide error-free decoding for any channel with
p \leq 0.42
and to yield code rates closer to capacity than those of Elias's original code. An heuristic algorithm is given for selecting an efficient set of BCH codes to iterate.