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Decoding a class of Lee metric codes over a Galois ring

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1 Author(s)
Byrne, E. ; Dept. of Math., Nat. Univ. of Ireland, Maynooth, Ireland

We investigate a class of Lee (1958) metric alternant codes with symbols in Zpn, establishing a lower bound on the minimum Lee distance where certain restrictions are placed on the code parameters. Corresponding to this bound, we have devised a decoding algorithm which is implemented over a finite field. The algorithm proceeds by finding a Grobner basis of the module M of solutions to a key equation. We obtain a necessary characterization of the solution module by solving iteratively a linear sequence over a Galois ring and show that the particular solution sought by the decoder is minimal in M. The required solution can then be found in an appropriate Grobner basis of M

Published in:

Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 4 )

Date of Publication:

Apr 2002

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