Title :
Grobner bases and alternant codes over Galois rings
Author :
Byrne, Eimear ; Fitzpatrick, Patrick
Author_Institution :
Dept. of Math, Nat. Univ. of Ireland, Cork, Ireland
Abstract :
We give a new algorithm for the solution of the Hamming metric decoding problem for alternant codes over a Galois ring R. First we develop a comprehensive theory of Grobner bases over R|x1,...,xn|, which is of independent interest. By specialising to the case of one variable, we show that the solution of the key equation can be determined as a certain minimal element in a Grobner basis of the solution module
Keywords :
Galois fields; codes; decoding; polynomials; Galois rings; Grobner bases; Hamming metric decoding; alternant codes; key equation; Analog computers; Decoding; Equations; Hamming distance; Interpolation; Mathematics; Parity check codes; Polynomials;
Conference_Titel :
Information Theory, 2000. Proceedings. IEEE International Symposium on
Conference_Location :
Sorrento
Print_ISBN :
0-7803-5857-0
DOI :
10.1109/ISIT.2000.866746
