7 research outputs found
A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes
Conflict-avoiding codes are used in the multiple-access collision channel
without feedback. The number of codewords in a conflict-avoiding code is the
number of potential users that can be supported in the system. In this paper, a
new upper bound on the size of conflict-avoiding codes is proved. This upper
bound is general in the sense that it is applicable to all code lengths and all
Hamming weights. Several existing constructions for conflict-avoiding codes,
which are known to be optimal for Hamming weights equal to four and five, are
shown to be optimal for all Hamming weights in general.Comment: 10 pages, 1 figur
Non-disjoint strong external difference families can have any number of sets
Strong external difference families (SEDFs) are much-studied combinatorial
objects motivated by an information security application. A well-known
conjecture states that only one abelian SEDF with more than 2 sets exists. We
show that if the disjointness condition is replaced by non-disjointness, then
abelian SEDFs can be constructed with more than 2 sets (indeed any number of
sets). We demonstrate that the non-disjoint analogue has striking differences
to, and connections with, the classical SEDF and arises naturally via another
coding application