The maximum size of a partial 3-spread in a finite vector space over GF(2)

S. El-Zanati; H. Jordon; G. Seelinger; P. Sissokho; L. Spence

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The maximum size of a partial 3-spread in a finite vector space over GF(2)

机译：GF（2）上有限向量空间中部分3展开的最大大小

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摘要

Let n ≥ 3 be an integer, let V_n (2) denote the vector space of dimension n over GF(2), and let c be the least residue of n modulo 3. We prove that the maximum number of 3-dimensional subspaces in V_n (2) with pairwise intersection (0) is 2~n-2~c/7 - c for n ≥ 8 and c = 2. (The cases c = 0 and c = 1 have already been settled.) We then use our results to construct new optimal orthogonal arrays and (s, k, λ)-nets.

机译：令n≥3为整数，令V_n（2）表示在GF（2）上维度n的向量空间，令c为n模3的最小残差。我们证明了3维子空间的最大数目当n≥8且c = 2时，具有成对相交（0）的V_n（2）为2〜n-2〜c / 7-c。（已经解决c = 0和c = 1的情况。）我们的结果构建了新的最佳正交阵列和（s，k，λ）-网络。

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来源
《Designs, Codes and Crytography》 |2010年第2期|101-107|共7页
作者
S. El-Zanati; H. Jordon; G. Seelinger; P. Sissokho; L. Spence;
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作者单位

4520 Mathematics Department, Illinois State University, Normal, IL 61790-4520, USA;

4520 Mathematics Department, Illinois State University, Normal, IL 61790-4520, USA;

4520 Mathematics Department, Illinois State University, Normal, IL 61790-4520, USA;

4520 Mathematics Department, Illinois State University, Normal, IL 61790-4520, USA;

4520 Mathematics Department, Illinois State University, Normal, IL 61790-4520, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
spreads; partial spreads; orthogonal arrays; (s, k, λ)-nets;

机译：点差部分利差;正交阵列（s;k;λ）-网;

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1. The maximum size of a partial 3-spread in a finite vector space over GF(2) [J] . S. El-Zanati, H. Jordon, G. Seelinger, Designs, Codes and Cryptography . 2010,第2期

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2. The maximum size of a partial spread in a finite projective space [J] . Ngstase Esmeralda L., Sissokho Papa A. Journal of Combinatorial Theory, Series A . 2017,第期

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3. Partitions of finite vector spaces over GF(2) into subspaces of dimensions 2 and s [J] . G. Seelinger, P. Sissokho, L. Spence, Finite fields and their applications . 2012,第6期

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The maximum size of a partial 3-spread in a finite vector space over GF(2)

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