Article ID Journal Published Year Pages File Type
4647170 Discrete Mathematics 2015 21 Pages PDF
Abstract
In this paper, we study the third weight of generalized Reed-Muller codes. Using results from Erickson, we prove under some 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. We are able to determine the third weight and the third weight codewords of generalized Reed-Muller codes of order r=a(q−1)+b with 2≤b≤q−1, for small b.
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Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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On the third weight of generalized Reed-Muller codes
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