Alexander Zeh – Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes


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Two generalizations of the Hartmann–Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed.
The first one is proven by embedding the given cyclic code into a cyclic product code.
Furthermore, we show that unique decoding up to this bound is always possible and outline a quadratic-time
syndrome-based error decoding algorithm. The second bound is stronger and the proof is more involved.
Our technique of embedding the code into a cyclic product code can be applied to other bounds, too and
therefore generalizes them.