Multichannel Conflict-Avoiding Codes of Weights Three and Four

Optimal conflict-avoiding codes of odd length and weight three

A conflict-avoiding code (CAC) of length n and weight k is a collection of binary vectors of length n and Hamming weight k, such that the inner product of any two vectors or their arbitrary cyclic shifts is at most one. In the study of multiple-access collision channel without feedback, CAC is used to guarantee that each transmitting user can send at least one data packet successfully during a ...

Strongly Conflict-Avoiding Codes

Strongly conflict-avoiding codes are used in the asynchronous multiple-access collision channel without feedback. The number of codewords in a strongly conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, an upper bound on the size of strongly conflictavoiding codes is proved. In addition, we provide an improved upper bound if the codes are...

Classification of optimal conflict-avoiding codes of weights 6 and 7

Constant Weight Conflict-Avoiding Codes

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 ∑ 0≤t≤n−1 xitxj,t+s ≤ 1 for any distinct codewords xi = (xi0, xi1, . . . , xi,n−1) and xj = (xj0, xj1, . . . , xj,n−1) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k is said to be optimal. A CAC has be...

Optimal strongly conflict-avoiding codes of even length and weight three

Strongly conflict-avoiding codes (SCACs) are employed in a slotasynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. Assume all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be suppo...