A powerful method for constructing difference families and optimal optical orthogonal codes
Designs, Codes and Cryptography
Some Constructions of Conflict-Avoiding Codes
Problems of Information Transmission
Constant Weight Conflict-Avoiding Codes
SIAM Journal on Discrete Mathematics
On Conflict-Avoiding Codes of Length n=4m for Three Active Users
IEEE Transactions on Information Theory
Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3
Designs, Codes and Cryptography
A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
Designs, Codes and Cryptography
A general upper bound on the size of constant-weight conflict-avoiding codes
IEEE Transactions on Information Theory
Optimal conflict-avoiding codes of even length and weight 3
IEEE Transactions on Information Theory
On cyclic 2(k -1)-support (n,k)k-1 difference families
Finite Fields and Their Applications
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A conflict-avoiding code (CAC) C of length n and weight k is a collection of k-subsets of $${\mathbb{Z}}_n$$ such that $$\Delta(x) \cap \Delta(y) = \emptyset$$ holds for any $$x,y\in C$$ , $$x\not= y$$ , where $$\Delta(x)=\{j-i\,|\, i,j\in x, i\not= j\}$$ . A CAC with maximum code size for given n and k is called optimal. Furthermore, an optimal CAC C is said to be tight equi-difference if $$\bigcup_{x\in C}\Delta(x)={\mathbb{Z}}_n\setminus \{0\}$$ holds and any codeword $$x\in C$$ has the form $$\{0,i,2i,\ldots,(k-1)i\}$$ . The concept of a CAC is motivated from applications in multiple-access communication systems. In this paper, we give a necessary and sufficient condition to construct tight equi-difference CACs of weight k = 3 and characterize the code length n's admitting the condition through a number theoretical approach.