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

Authors:
Johannes Maks;Juriaan Simonis
Affiliations:
Delft University of Technology, Faculty of Information Technology and Systems, Department of Mediamatics, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Faculty of Information Technology and Systems, Department of Mediamatics, P.O. Box 5031, 2600 GA Delft, The Netherlands
Venue:
Designs, Codes and Cryptography
Year:
2000

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Abstract

There are exactlytwo non-equivalent [32,11,12]-codes in the binaryReed-Muller code {\cal{RM}}(2,5) which contain {\cal{RM}}(1,5)and have the weight set \{0,12,16,20,32\}. Alternatively,the 4-spaces in the projective space {\Bbb{P}}(\Lambda^{2}{\Bbb{F}}_{2}^{5})over the vector space \Lambda^{2}{\Bbb{F}}_{2}^{5}for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on{\Bbb{P}} (\Lambda^{2}{\Bbb{F}}_{2}^{5}).