Product codes and the singleton bound
Minimum distance is not always the most determinant factor to acheive high performance for error correction. Of course the knowledge of the whole weight distribution of the code is more accurate than the knowledge of the mere minimum distance, and the phenomenon amplifies for a high noise level. Besides this fact, the use of error-correcting codes in practical situations requires a trade-off between the algorithmic complexity and the performance of the decoding procedure. We show here that for low rates a very good trade-off is possible using product codes, although they are known for their poor minimum distance.
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