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On the third weight of generalized Reed-Muller codes (1401.5234v1)
Published 21 Jan 2014 in cs.IT, math.IT, and math.NT
Abstract: In this paper, we study the third weight of generalized Reed-Muller codes. We prove under some restrictive condition that the third weight of generalized Reed-Muller codes depends on the third weight of generalized Reed-Muller codes of small order with two variables. In some cases, we are able to determine the third weight and the third weight codewords of generalized Reed-Muller codes.