### Abstract

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).

Original language | English |
---|---|

Pages (from-to) | 504-507 |

Number of pages | 4 |

Journal | IEEE Transactions on Information Theory |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1994 Mar |

### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

## Cite this

Song, H. Y., & Golomb, S. W. (1994). Some New Constructions for Simplex Codes.

*IEEE Transactions on Information Theory*,*40*(2), 504-507. https://doi.org/10.1109/18.312174