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TitleAlgebraic decoding of negacyclic codes over $mathbb Z_4$.
Author(s) Eimear Byrne, Marcus Greferath, Jaume Pernas, Jens Zumbrägel
TypeArticle in Journal
AbstractIn this article we investigate Berlekampís negacyclic codes and discover that these codes, when considered over the integers modulo 4, do not suffer any of the restrictions on the minimum distance observed in Berlekampís original papers: our codes have minimum Lee distance at least 2t + 1, where the generator polynomial of the code has roots α, α 3, . . . , α 2t-1 for a primitive 2nth root α of unity in a Galois extension of ℤ4 ; no restriction on t is imposed. We present an algebraic decoding algorithm for this class of codes that corrects any error pattern of Lee weight ≤ t. Our treatment uses Gröbner bases, the decoding complexity is quadratic in t.
KeywordsNegacyclic code, Integers modulo 4, Lee metric, Galois ring, Decoding, Gröbner bases, Key equation, Solution by approximations, Module of solutions
ISSN0925-1022; 1573-7586/e
URL http://link.springer.com/article/10.1007%2Fs10623-012-9632-3
JournalDes. Codes Cryptography
PublisherSpringer US, New York, NY
Translation No
Refereed No