### Abstract

We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in the form of Cayley graphs; and (2) embedding the group into a binary space using some of their permutation representations by providing the generators with realization of permutations of some terms. The proposed codes are endowed with some good characteristics as follows: (a) we can easily learn information about the distances of the obtained codes, and moreover, (b) we can establish a decoding method for them that can correct random errors whose distances from code words are less than half of the minimum distances achieved using only parity checking procedures.

Original language | English |
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Pages (from-to) | 2734-2744 |

Number of pages | 11 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E88-A |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 2005 |

Externally published | Yes |

### Keywords

- Buckminster Fullerene
- Cayley graphs
- Nonlinear binary codes of constant weights
- Permutation representations

### ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics