Harmonic Distributions for Equitable Partitions of a Hypercube |
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Authors: | Jong Yoon Hyun |
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Affiliation: | 1. Institute of Mathematical Science, Ewha Womans University, 11‐1, Daehyun‐Dong, Seodaemun‐Gu, Seoul, S. KoreaThe results in the paper were presented in part at KIAS International Conference on Coding Theory and Applications, 2012, Seoul, Korea, Nov. Contract grant sponsor: National Research Foundation of Korea (NRF);2. contract grant sponsor: Korea government(MEST);3. contrant grant number: 2011‐0010328. |
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Abstract: | We provide general criteria for orthogonal arrays and t‐designs on equitable partitions of a hypercube by exploring harmonic distributions. Generalized harmonic weight enumerators for real‐valued functions of are introduced and applied to eigenfunctions of the adjacency matrix of . Using this, expressions for harmonic distributions are established for every cell of an equitable partition π of . Moreover, for any given cell in the partition π, the strength of the cell as an orthogonal array is explicitly expressed, and also a characterization of a t‐design of that cell is established. We also compute strengths of cells and find t‐designs from cells based on constructions of Krotov, Borges, Rifa, and Zinoviev. |
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Keywords: | harmonic weight enumerator harmonic distribution equitable partition completely regular code eigenfunction orthogonal array t‐design |
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