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- W2074719346 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 , 2 k − 1) is determined for all sufficiently large n satisfying either n ≡ 1 mod k and n ( n − 1) ≡ 0 mod 2 k 2 , 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." @default.
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- W2074719346 date "2014-10-09" @default.
- W2074719346 modified "2023-09-26" @default.
- W2074719346 title "Optimal Codes in the Enomoto-Katona Space" @default.
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- W2074719346 doi "https://doi.org/10.1017/s0963548314000509" @default.
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