Algebraic Decoding Techniques by Using Grobner Bases

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9314347 Reed This is a program of research including four inter-related topics. (1) decoding techniques and Grobner bases: a polynomial point of view (2) decoding cyclic codes up to their true minimum distance, (3) decoding algebraic geometry codes, and (4) simplified decoding algorithms. The decoding problem will be formulated in terms of ideals, and relationships with the error locator polynomial and Grobner bases will be sought. Preliminary results show that is is possible to construct algebraic decoding methods by the use of Grobner bases to decode all cyclic codes up to the true minimum distance in some special cases. These techniques promise to be useful as a means of decoding algebraic geometry codes. Much effort in complexity analysis will be needed here. The overall goal is to come up with a low complexity decoding algorithm that corrects up to the true minimum distance. ***