Fredman-Kolmo´s bounds and information theory
SIAM Journal on Algebraic and Discrete Methods
Separating partition systems and locally different sequences
SIAM Journal on Discrete Mathematics
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
IEEE Transactions on Information Theory
New rate pairs in the zero-error capacity region of the binary multiplying channel without feedback
IEEE Transactions on Information Theory
On the maximum size of (P,Q)-free families
Discrete Mathematics - Kleitman and combinatorics: a celebration
Self-Similarity Bounds for Locally Thin Set Families
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
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Let M(n, A) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly two of them have a 1. We prove that M(n, A) ≤ 20.78n for all sufficiently large n. Let M(n, C) denote the maximum possible cardinality of a family of binary strings of length n, such that for every four distinct members of the family there is a coordinate in which exactly one of them has a 1. We show that there is an absolute constant c M(n, C) ≤ 2cn for all sufficiently large n. Some related questions are discussed as well.