Three constructions for n-dimensional regular simplex codes i, 0 < i < n, are proposed, two of which have the property that αi,- for 1 < i < n is a cyclic shift of a1. 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 (”, k, A) cyclic (or Abelian) difference set exists, this method is generalized so that a similar method is shown to work with v = n (the number of dimensions).
Bibliographical noteFunding Information:
Manuscript received November 4, 1992: revised May 6, 1993. This work was supported in part by the United States Office of Naval Research under Grant Numbei N00014-90-5-1341. The author!. are with the Department of EE-Systems, Communication Sciences Institute, University of Southern California, Los Angeles, CA 90089 USA. IEEE Log Number 9215440.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences