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>A subspace code of size egin{document}$ f{333} $end{document} in the setting of a binary egin{document}$ f{q} $end{document}-analog of the Fano plane
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A subspace code of size egin{document}$ f{333} $end{document} in the setting of a binary egin{document}$ f{q} $end{document}-analog of the Fano plane
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机译：子空间代码<内联公式> begin {document} $ bf {333} $ bf {333} $ nod {document} 二进制<内联公式> begin {document} $ bf {q} $ end {document} - Fano平面的模拟
We show that there is a binary subspace code of constant dimension~3 inambient dimension 7, having minimum distance 4 and cardinality 333, i.e., $333le A_2(7,4;3)$, which improves the previous best known lower bound of 329.Moreover, if a code with these parameters has at least 333 elements, itsautomorphism group is in $31$ conjugacy classes. This is achieved by a moregeneral technique for an exhaustive search in a finite group that does notdepend on the enumeration of all subgroups.
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机译：我们表明存在恒定尺寸〜3烟囱尺寸7的二进制子空间码，具有最小距离4和基数333，即333美元 Le A_2（7,4; 3）$，这提高了以前最知名的下限329.Moreover，如果具有这些参数的代码至少有333个元素，Itsautomorphism组是31美元的$共轭课程。这是通过一种更加全面的技术来实现的，用于在有限组中进行详尽的搜索，该有限组在所有子组的枚举上没有。
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机译：长度<内联公式> begin {document} $ np ^ s $ new {document} over <内联 - 公式> begin {document} $ mathbb {f} _ {p ^ m} + u mathbb {f} _ {p ^ m} $ end {document}
