In a recent book (Elements of Digital Satellite Communication, vol.II, 1985), W.W. Wu has shown that all the secret-sharing systems known at the time his book was written can be described in terms of Reed-Solomon codes. He has also remarked that all are connected with latin squares and has illustrated this remark by means of examples. However, his examples construct secret-sharing systems in which the secret can be unlocked with only two keys. It is shown here that this is necessarily the case when latin squares are used. For this purpose. Wu's observations are replaced by a theorem, one which also shows a connection with Golomb-Posner codes.>

It is shown how row-complete Latin squares and Tuscan squares can be used to construct nonbinary 1-D and 2-D arrays that have the u*v horizontal and/or vertical window property for all sufficiently large windows. It is shown how binary arrays with a similar property can be derived. Since an array can only be a perfect map for one particular size of window, the arrays that are constructed are not perfect but nevertheless have several practical applications, among others in connection with the coding and transmission of pictures. The method is deterministic rather than stochastic, and the arrays derived contain an effectively random selection of the windows of each relevant size.>

Several ways of allocating frequencies efficiently are suggested that are based on the use of Latin squares. A Latin square of order n is a square array of n rows and n columns, and involving n symbols each of which occurs n times within the square in such a way that all the different symbols occur once in each row and once in each column. This approach provides two alternative ways of arranging the transmitters for a mobile radio telephone system, one rectangular and the other close-packed hexagonal. In both cases optimal patterns for frequency allocation result. A solution using the least-possible number of frequencies for each case is given, as well as one that is ideal in the sense that all the transmitters that surround any particular one are provided with distinct frequencies.>