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A new lower bound for the distance of cyclic codes is proposed. This bound depends on the defining set of the code, like several other bounds. The proposed bound improves upon the Bose-Chaudhuri-Hocquehghen (BCH) bound and, for some codes, improves upon the Hartmann-Tzeng bound and the Roos bound as well

Our purpose is to recall some basic aspects about linear and cyclic codes. We first briefly describe the role of error-correcting codes in communication. To do this we introduce, with examples, the concept of linear codes and their parameters, in particular the Hamming distance. A fundamental subclass of linear codes is given by cyclic codes, that enjoy a… (More)

- Emanuele Betti
- 2006

M ANY lower bounds exist for the minimum Hamming distance of cyclic codes, among others the BCH [2], Hartmann-Tzeng [3], and Roos [4] bounds. They are usually based on patterns in the complete defining set of the code. We present a similar bound, which is based on a pattern which has never been noted before. Our lower bound is stronger than the BCH bound,… (More)

— In this paper a new lower bound for the distance of cyclic codes is proposed. This bound depends on the defining set of the code, like several other bounds. Moreover it is stronger than the BCH bound, but not stronger than the HT bound, yet it is not weaker than the Roos bound. I. INTRODUCTION Many lower bounds exist for the distance of cyclic codes,… (More)

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