Complexity of dependencies in bounded domains, Armstrong Codes, and generalizations
IEEE Transactions on Information Theory（2019）
摘要
The study of Armstrong codes is motivated by the problem of understanding complexities of dependencies in relational database systems, where attributes have bounded domains. A (q, k, n)-Armstrong code is a q-ary code of length n with minimum Hamming distance n - k + 1, and for any set of k - 1 coordinates there exist two codewords that agree exactly there. Let f(q, k) be the maximum n for which such a code exists. In this paper, f(q, 3) = 3q - 1 is determined for all q ≥ 5 with three possible exceptions. This disproves a conjecture of Sali. Further, we introduce generalized Armstrong codes for branching, or (s, t)-dependencies and construct several classes of optimal Armstrong codes in this more general setting.
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关键词
relational database systems,armstrong codes,relational databases,relational database,optimal armstrong codes,relational database system,t)-dependences,(s,n)-armstrong code,minimum hamming distance,bounded domain dependence complexity,q-ary code,generalized armstrong codes,codes,codewords,hamming codes,extorthogonal double covers,lower bounds,functional dependency,k-1 coordinates,(q,bounded domains,sali conjecture,k,dependency complexity,knowledge based systems,upper bound,information theory
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