Some new constructions for simplex codes
Hong‐Yeop Song, S. W. Golomb · IEEE Transactions on Information Theory · 1994
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).>