Harmonic Index t-Designs in the Hamming Scheme for Arbitrary q
Harmonic Index t-Designs in the Hamming Scheme for Arbitrary q
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DOI：
10.1007/s00373-020-02170-z
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发表时间：
2020-04
影响因子：
0.7
通讯作者：
M. Tagami;Ryota Hori
中科院分区：
文献类型：
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作者：
M. Tagami;Ryota Hori
对称关联方案中的t -设计概念是由Delsarte提出的。谐波索引设计是指索引由单个索引组成的特殊情况。Zhu等人研究了二进制Hamming格式中的调和指数设计，并给出了基数的Fisher型下界。在此基础上定义了紧谐指标设计的概念，并考虑了分类问题。本文将其结果推广到一般的Hamming格式，并对其Fisher型下界进行了改进。利用改进的Fisher下界，重新定义了紧谐指标设计的概念，并考虑了分类问题。此外，我们给出了调和指数设计的一个自然表征，并给出了bannaii - okuda - tagami给出的构造球面调和指数设计的Hamming格式的类比。
The notion ofT-design in a symmetric association scheme was introduced by Delsarte. A harmonic indext-design is the particular case in which the index setTconsists of a single index. Zhu et al. studied a harmonic indext-design in the binary Hamming scheme and gave a Fisher type lower bound on the cardinality. Also they defined the notion of a tight harmonic index design using the bound, and considered the classification problem. In this paper, we extend their results to the general Hamming scheme and improve their Fisher type lower bound slightly. Also using the improved Fisher type lower bound, we redefine the notion of a tight harmonic index design and consider the classification problem. Furthermore, we give a natural characterization for a harmonic indext-design and an analogue in the Hamming scheme for the construction of spherical harmonic indext-designs which was given by Bannai–Okuda–Tagami.