# Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes

@article{Zeh2013GeneralizingBO, title={Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes}, author={Alexander Zeh and Antonia Wachter-Zeh and Maximilien Gadouleau and Sergey V. Bezzateev}, journal={2013 IEEE International Symposium on Information Theory}, year={2013}, pages={126-130} }

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…

## 8 Citations

### New bounds on the minimum distance of cyclic codes

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Two bounds on the minimum distance of cyclic codes are proposed, one generalizes the Roos bound and the other uses a second cyclic code, namely the non-zero-locator code, but is not directly related to cyclic product codes.

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Some results are presented on a generalization of a method to obtain new lower bounds on the minimum distance of cyclic codes over finite fields that applies to several examples ofcyclic codes.

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- Computer ScienceFinite Fields Their Appl.
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### Spectral analysis of quasi-cyclic product codes

- Computer Science, Mathematics2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

The spectralAnalysis of a quasi-cyclic product code in terms of the spectral analysis of the row- and the column-code is given and a new lower bound on the minimum Hamming distance of a given quasi- cyclic code is provided.

### A survey on product codes and 2-D codes

- Computer ScienceArXiv
- 2021

This note surveys cyclic product codes, direct product of various generalizations of cyclic codes and their properties.

### Algebraic soft- and hard-decision decoding of generalized reed-solomon and cyclic codes

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- 2013

The reformulation of the interpolation-based approach in terms of Key Equations for Generalized Reed--Solomon codes for both, the hard-dec decision variant by Guruswami--Sudan, as well as for the soft-decision approach by Kotter--Vardy are reformulated.

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