Optimal Subcodes of Second Order Reed-Muller Codes andMaximal Linear Spaces of Bivectors of Maximal Rank期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Optimal Subcodes of Second Order Reed-Muller Codes andMaximal Linear Spaces of Bivectors of Maximal Rank

Authors:	Johannes Maks Juriaan Simonis

Institution:	(1) Faculty of InformationTechnology and Systems, Department of Mediamatics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands

Abstract:	There are exactlytwo non-equivalent 32,11,12]-codes in the binaryReed-Muller code $\mathcal{R}\mathcal{M}(2,5)$ which contain $\mathcal{R}\mathcal{M}(2,5)$ and have the weight set {0,12,16,20,32}. Alternatively,the 4-spaces in the projective space $\mathbb{P}(\Lambda ^2 \mathbb{F}_2^5 )$ over the vector space $\mathbb{P}(\Lambda ^2 \mathbb{F}_2^5 )$ for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on $\mathbb{P}(\Lambda ^2 \mathbb{F}_2^5 )$ .

Keywords:	Reed-Muller codes BCH codes rank loci symplectic spaces
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