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Some new constructions for simplex codes

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2 Author(s)
Song, H.Y. ; Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA ; Golomb, S.W.

Three constructions for n-dimensional regular simplex codes αi, 0⩽i⩽n, are proposed, two of which have the property that αi for 1⩽i⩽n is a cyclic shift of α1. 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,λ) cyclic (or Abelian) difference set exists, this method is generalized so that a similar method is shown to work with ν=n (the number of dimensions)

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Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 2 )