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 \(\mathbb{P}(\Lambda ^2 \mathbb{F}_2^5 )\).
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Maks, J., Simonis, J. Optimal Subcodes of Second Order Reed-Muller Codes andMaximal Linear Spaces of Bivectors of Maximal Rank. Designs, Codes and Cryptography 21, 165–180 (2000). https://doi.org/10.1023/A:1008343829143
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DOI: https://doi.org/10.1023/A:1008343829143