Some results on the problem of constructing asymptotically good error-correcting codes

Justesen has shown that concatenating a class of binary codes with a Reed-Solomon (RS) code produces asymptotically good codes. For low rates, the value of the ratio of minimum distance to code length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(d/n)</tex> for such codes is substantially lower than that known to be achievable by the Zyablov bound. In this paper, we present a small class of binary codes with some useful properties. This class is then used in Justesen's construction to produce codes that have relatively large values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d/n</tex> for low rates.