Abstract:We give a short account of the construction and properties of left neofields. Most useful in practice seem to be neofields based on the cyclic group and particularly those having an additional divisibility property, called {D-neofields}. We shall give examples of applications to the construction of orthogonal latin squares, to the design of tournaments balanced for residual effects and to cryptography.
Keywords: neofield, loop, orthomorphism, complete mapping, orthogonal latin squares, cryptography, balanced round robin tournament
AMS Subject Classification: 12K99, 20N05, 05B15, 05B30, 94A60