Lifting Decoding Schemes over a Galois Ring

Authors:
Eimear Byrne
Affiliations:
-
Venue:
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2001

Citing 5
Cited 0

Gro¨bner bases: a computational approach to commutative algebra

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Efficient decoding of Zpk-linear codes

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On the key equation

IEEE Transactions on Information Theory

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Abstract

Any vector with components in a Galois ring R = GR(pm, n) has a unique p-adic representation, given a tranversal on the cosets of {p} in R. We exploit this representation to lift a decoding algorithm for an associated code over the residue field of R to a decoding scheme for the original code. The lifted algorithm involves n consecutive applications of the given procedure. We apply these techniques to the decoding of an alternant code over a Galois ring.