The Bose-Chaudhuri-Hocquenghem (BCH, 1960) bound d_{BCH} is the oldest bound on the minimum distance of cyclic codes and it allows a syndrome-based algebraic decoding up to (d_{BCH}-1)/2$ errors. Generalizations of the BCH bound are the Hartmann-Tzeng (HT, 1972) and the Roos (1980) bound.
Recently, a new approach that allows a simple decoding up to a new bound was developed by Zeh, Wachter-Zeh and Bezzateev (ZWB, 2011). This new bound improves upon the HT bound for several classes of cyclic codes.
In a first step the existing bounds for all binary cyclic codes (up to a length of n=63) and the new ZWB bound should be calculated.
In this Bachelor's thesis efficient algorithms for calculating the bounds of cyclic codes are discussed. Furthermore, a generalization of the ZWB and the connection of this approach to existing bounds is developed.