Decoding a bit more than the BCH bound
The concept and characterization of ε-best rational approximations (ε-BRA) are given in this paper. And, by using this concept, a decoding algorithm for some cyclic codes is presented.
The conventional algorithms (Berlekamp-Massey, Continued Fraction, Extended Euclidean, ...) allows us to correct up to eBCH≤d−1/2 errors where d is the designed minimum distance of the cyclic code. However our algorithm will be able to correct more than d−1/2 errors in case that the true distance δ be greater than d.
The Expurged Golay Code is a very good example of the algorithm presented which allows us to correct up to three errors. This code G(23,11) is 3-error correcting but, by using the conventional algorithms we can only correct up to two errors.
KeywordsCyclic Codes Expurged Golay Code Continued Fraction Expansion Convergents ε-BRA Rational Approximations
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