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A new Yang number and consequences

机译:一个新的杨数和后果

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Base sequences BS(m, n) are quadruples (A; B; C; D) of {±1}-sequences, A and B of length m and C and D of length n, the sum of whose non-periodic auto-correlation functions is zero. Base sequences and some special subclasses of BS(n + 1, n) known as normal and near-normal sequences, NS(n) and NN(n), as well as T-sequences and orthogonal designs play a prominent role in modern constructions of Hadamard matrices. In our previous papers (Ðoković, Classification of near-normal sequences, arXiv:0903.4390v1 [math.CO] 25 Mar (2009); Ðoković, Some new near-normal sequences, arXiv:0907.3129v1 [math.CO] 17 Jul (2009)) we have classified the near-normal sequences NN(s) for all even integers s ≤ 32 (they do not exist for odd s > 1). We now extend the classification to the case s = 34. Moreover we construct the first example of near-normal sequences NN(36). Consequently, we construct for the first time T-sequences of length 73. For all smaller lengths, T-sequences were already known. Another consequence is that 73 is a Yang number, and a few important consequences of this fact are given. Keywords Base sequences - Near-normal sequences - T-sequences - Hadamard matrices - Orthogonal designs Mathematics Subject Classification (2000) 05B20 - 05B30 Communicated by Charles J Colbourn.
机译:基本序列BS(m,n)是{±1}序列的四倍(A; B; C; D),长度为m的A和B,长度为n的C和D,它们的非周期自动序列之和相关函数为零。 BS(n + 1,n)的基本序列和某些特殊子类称为正常序列和接近正常序列,NS(n)和NN(n)以及T序列和正交设计在现代结构中起着重要作用哈达玛矩阵。在我们之前的论文中(Ðoković,接近正常序列的分类,arXiv:0903.4390v1 [math.CO],2009年3月25日;Ðoković,一些新的接近正常序列,arXiv:0907.3129v1 [math.CO],7月17日( 2009年)),我们对所有s≤32的所有偶数整数(几乎不存在奇数s> 1的情况)进行了分类。现在,我们将分类扩展到s = 34的情况。此外,我们构造了接近法线序列NN(36)的第一个示例。因此,我们首次构造了长度为73的T序列。对于所有较小的长度,T序列都是已知的。另一个结果是73是一个Yang数,并且给出了这个事实的一些重要结果。关键词基本序列-接近正规序列-T序列-Hadamard矩阵-正交设计数学主题分类(2000)05B20-05B30由Charles J Colbourn进行通信。

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