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New families of atomic Latin squares and perfect 1-factorisations
A perfect 1-factorisation of a graph G is a decomposition of G into edge disjoint 1-factors such that the union of any two of the factors is a Hamiltonian cycle. Let p ≥ 11 be prime. We demonstrate the existence of two non-isomorphic perfect 1-...
On non-existence of perfect and nearly perfect sequences
We study the complex p-ary perfect and nearly perfect sequences where p is an odd prime and show that the existence of such sequences is equivalent to the existence of certain kinds of difference sets. Using results from difference sets, there are no p-...
Transitive nonpropelinear perfect codes
A code is called transitive if its automorphism group (the isometry group) of the code acts transitively on its codewords. If there is a subgroup of the automorphism group acting regularly on the code, the code is called propelinear. Using Magma ...






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