Z4‐Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line‐Sets
Z4‐Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line‐Sets
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DOI：
10.1112/s0024611597000403
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发表时间：
1997-09
影响因子：
1.8
通讯作者：
A. Calderbank;P. Cameron;W. Kantor;JJ Seidel
中科院分区：
文献类型：
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作者：
A. Calderbank;P. Cameron;W. Kantor;JJ Seidel
当 m 为奇数时，Ω+(2m + 2,2) 类型的正交向量空间中的扩展与二进制 Kerdock 码和具有规定角度的 2m + 1 中的极值线集相关。 2m 维二元辛向量空间中的扩展与 Z4 上的 Kerdock 码以及具有规定角度的 \CC2m 中的极值线集相关。这些联系涉及与超特殊 2 群相关的二元、实数和复杂几何。显示了从辛到正交展开的几何图，以将灰度图从相应的 Z4-Kerdock 代码导出到其二进制图像。这些几何考虑导致了对于任何奇数复合 m 的大量 Z4-Kerdock 代码的构造。他们还生产新的 Z4-线性 Kerdock 和 Preparata 代码。 1991年数学科目分类：初级94B60； secondary 51M15, 20C99.
When m is odd, spreads in an orthogonal vector space of type Ω+(2m + 2,2) are related to binary Kerdock codes and extremal line‐sets in 2m + 1 with prescribed angles. Spreads in a 2m‐dimensional binary symplectic vector space are related to Kerdock codes over Z4 and extremal line‐sets in \CC2m with prescribed angles. These connections involve binary, real and complex geometry associated with extraspecial 2‐groups. A geometric map from symplectic to orthogonal spreads is shown to induce the Gray map from a corresponding Z4‐Kerdock code to its binary image. These geometric considerations lead to the construction, for any odd composite m, of large numbers of Z4‐Kerdock codes. They also produce new Z4‐linear Kerdock and Preparata codes. 1991 Mathematics Subject Classification: primary 94B60; secondary 51M15, 20C99.