抄録
type:text
Let X be a nite set in a complex sphere of d dimension. Let D(X) be the set of usual inner products of two distinct vectors in X. A set X is called a complex spherical s-code if the cardinality of D(X) is s and D(X) contains an imaginary number. We would like to classify the largest possible s-codes for given dimension d. In this paper, we consider the problem for the case s = 3. Roy and Suda (2014) gave a certain upper bound for the cardinalities of 3-codes. A 3-code X is said to be tight if X attains the bound. We show that there exists no tight 3-code except for dimensions 1, 2. Moreover we make an algorithm to classify the largest 3-codes by considering representations of oriented graphs. By this algorithm, the largest 3-codes are classi ed for dimensions 1, 2, 3 with a current computer.
収録刊行物
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- Discrete & Computational Geometry
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Discrete & Computational Geometry 60 (2), 294-317, 2018-09
Springer US
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詳細情報 詳細情報について
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- CRID
- 1050282813763970944
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- NII論文ID
- 120006729497
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- ISSN
- 01795376
- 14320444
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- 本文言語コード
- en
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- 資料種別
- journal article
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- データソース種別
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