Abstract
Three constructions for n-dimensional regular simplex codes /spl alpha//sub i/, 0/spl les/i/spl les/n, are proposed, two of which have the property that /spl alpha//sub i/ for 1/spl les/i/spl les/n is a cyclic shift of /spl alpha//sub 1/. The first method is shown to work for all the positive integers n=1,2,... using only three real values. It turns out that these values are rational whenever n+1 is a square of some integer. Whenever a (v,k,/spl lambda/) cyclic (or Abelian) difference set exists, this method is generalized so that a similar method is shown to work with /spl nu/=n (the number of dimensions).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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