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Minimum distance of relative Reed–Muller codes
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Minimum distance of relative Reed–Muller codes
Tohru Nakashima1 
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Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women’s University, Mejirodai, Bunkyoku, Tokyo 112-8681, Japan |
Received: 9 February 2005 Revised: 7 December 2007 Published online: 10 March 2009
Abstract We describe a construction of error-correcting codes on a fibration over a curve defined over a finite field, which may be
considered as a relative version of the classical Reed–Muller code. In the case of complete intersections in a projective
bundle, we give an explicit lower bound for the minimum distance.
Keywords Error-correcting codes - Relative Reed–Muller codes - Semistable vector bundles
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