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 ofC(n,k,d), the size of an optimal code of lengthn, weightk, and distancedin the Enomoto-Katona space. The value ofC(n,k,d) was known only for some congruence classes ofnwhen (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 largensatisfying eithern≡ 1 modkandn(n− 1) ≡ 0 mod 2k2, orn≡ 0 modk. We also give complete solutions fork= 2 and determineC(n,3,5) for certain congruence classes ofnwith finite exceptions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
