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- The Hamming scheme, named after Richard Hamming, is also known as the hyper-cubic association scheme, and it is the most important example for coding theory. In this scheme the set of binary vectors of length and two vectors are -th associates if they are Hamming distance apart. Recall that an association scheme is visualized as a complete graph with labeled edges. The graph has vertices, one for each point of and the edge joining vertices and is labeled if and are -th associates. Each edge has a unique label, and the number of triangles with a fixed base labeled having the other edges labeled and is a constant depending on but not on the choice of the base. In particular, each vertex is incident with exactly edges labeled ; is the valency of the relation The in a Hamming scheme are given by Here, and The matrices in the Bose-Mesner algebra are matrices, with rows and columns labeled by vectors In particular the -th entry of is if and only if (en)
- 조합론에서 해밍 결합 도식(Hamming結合圖式, 영어: Hamming association scheme)은 해밍 거리가 주어진 곱집합으로 구성된 결합 도식이다. (ko)
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- 2474 (xsd:nonNegativeInteger)
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- 조합론에서 해밍 결합 도식(Hamming結合圖式, 영어: Hamming association scheme)은 해밍 거리가 주어진 곱집합으로 구성된 결합 도식이다. (ko)
- The Hamming scheme, named after Richard Hamming, is also known as the hyper-cubic association scheme, and it is the most important example for coding theory. In this scheme the set of binary vectors of length and two vectors are -th associates if they are Hamming distance apart. Here, and The matrices in the Bose-Mesner algebra are matrices, with rows and columns labeled by vectors In particular the -th entry of is if and only if (en)
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- Hamming scheme (en)
- 해밍 결합 도식 (ko)
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