Abstract
Any vector with components in a Galois ring R = GR(p m, n) has a unique p-adic representation, given a tranversal on the cosets of ćpć 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.
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Byrne, E. (2001). Lifting Decoding Schemes over a Galois Ring. In: BoztaÅ, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_34
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DOI: https://doi.org/10.1007/3-540-45624-4_34
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