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Title: Optimal codes in the Enomoto-Katona space
Authors: Chee, Yeow Meng
Kiah, Han Mao
Zhang, Hui
Zhang, Xiande
Keywords: DRNTU::Engineering::Mathematics and analysis
Issue Date: 2014
Source: Chee, Y. M., Kiah, H. M., Zhang, H., & Zhang, X. Optimal codes in the Enomoto-Katona space. Combinatorics, probability and computing, 24(2), 382-406.
Series/Report no.: Combinatorics, probability and computing
Abstract: Coding in a new metric space, called the Enomoto-Katona space, has recently been considered in connection with the study of implication structures of functional dependencies and their generalizations in relational databases. The central problem is the determination of C(n,k,d), the size of an optimal code of length n, weight k, and distance d in the Enomoto-Katona space. The value of C(n,k,d) was known only for some congruence classes of n when (k,d) ∈ {(2,3),(3,5)}. In this paper, we obtain new infinite families of optimal codes in the Enomoto-Katona space and verify a conjecture of Brightwell and Katona in certain instances. In particular, C(n,k, 2k − 1) is determined for all sufficiently large n satisfying either n ≡ 1 mod k and n(n − 1) ≡ 0 mod 2k2, or n ≡ 0 mod k. We also give complete solutions for k = 2 and determine C(n,3,5) for certain congruence classes of n with finite exceptions.
DOI: 10.1017/S0963548314000509
Rights: © 2014 Cambridge University Press. This paper was published in Combinatorics, Probability and Computing and is made available as an electronic reprint (preprint) with permission of Cambridge University Press. The paper can be found at the following official DOI:  One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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