Designs, Codes and Cryptography
Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3
Designs, Codes and Cryptography
Design and construction of protocol sequences: shift invariance and user irrepressibility
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
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
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
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 $n$ with weight $k$ is a family of binary sequences of length $n$ and weight $k$ satisfying $\sum_{0\le t\le n-1}x_{it}x_{j,t+s}\le \lambda$ for any distinct codewords $x_i=(x_{i0},x_{i1},\ldots,x_{i,n-1})$ and $x_j=(x_{j0},x_{j1},\ldots,x_{j,n-1})$ in $C$ and for any integer $s$, where the subscripts are taken modulo $n$. A CAC with maximum code size for given $n$ and $k$ is said to be optimal. A CAC has been studied for sending messages correctly through a multiple-access channel. The use of an optimal CAC enables the largest possible number of potential users to transmit information efficiently and reliably. In this paper, the case $\lambda=1$ is treated, and various direct and recursive constructions of optimal CACs for weight $k=4$ and $5$ are obtained by providing constructions of CACs for general weight $k$. In particular, the maximum code size of CACs satisfying certain sufficient conditions is determined through number theoretical and combinatorial approaches.