Decoding of Interleaved Alternant Codes

Interpolation-based Decoding of Alternant Codes

We formulate the classical decoding algorithm of alternant codes afresh based on interpolation as in Sudan’s list decoding of Reed-Solomon codes, and thus get rid of the key equation and the linear recurring sequences in the theory. The result is a streamlined exposition of the decoding algorithm using a bit of the theory of Gröbner bases of modules.

On PGZ decoding of alternant codes

In this note we first review the classical Petterson-Gorenstein-Zierler decoding algorithm for the class of alternant codes (which includes Reed-Solomon, Bose-Chaudhuri-Hocquenghem and classical Goppa codes), then we present an improvement of the method to find the number of errors and the errorlocator polynomial, and finally we illustrate the procedure with several examples. In two appendices ...

Decoding a Class of Alternant Codes for the Lee Metric

Following are the abstracts of contributions (i.e., talks and posters) to the 13th Annual Meeting of the IMS held at the National University of Ireland Maynooth, 6–8 September 2000. The abbreviations after the names designate: ‘M’ for main speaker, ‘S’ for speaker, ‘RS’ for research student, and ‘P’ for poster. The abstracts are included as provided by the contributors for this volume of the Bu...

On Efficient Decoding of Alternant Codes over a Commutative Ring

Improved Decoding of Interleaved AG Codes

We analyze a generalization of a recent algorithm of Bleichenbacher et al. for decoding interleaved codes on the Q-ary symmetric channel for large Q. We will show that for any m and any the new algorithms can decode up to a fraction of at least βm βm+1 (1−R−2Q−1/2m)− errors, where β = ln(qm−1) ln(qm) , and that the error probability of the decoder is upper bounded by O(1/q ), where n is the blo...