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dc.contributor.authorChee, Yeow Mengen
dc.contributor.authorKiah, Han Maoen
dc.contributor.authorZhang, Huien
dc.contributor.authorZhang, Xiandeen
dc.identifier.citationChee, Y. M., Kiah, H. M., Zhang, H., & Zhang, X. Optimal codes in the Enomoto-Katona space. Combinatorics, probability and computing, 24(2), 382-406.en
dc.description.abstractCoding 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.en
dc.relation.ispartofseriesCombinatorics, probability and computingen
dc.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.en
dc.subjectDRNTU::Engineering::Mathematics and analysisen
dc.titleOptimal codes in the Enomoto-Katona spaceen
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen
dc.description.versionPublished versionen
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