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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, the authors 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. Their technique of embedding the code into a cyclic product code can be applied to other bounds, too and therefore generalizes them.
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