## Title data

Byrne, Eimear ; Kiermaier, Michael ; Sneyd, Alison:

**Properties of codes with two homogeneous weights.**

*In:* Finite Fields and their Applications.
Vol. 18
(2012)
Issue 4
.
- pp. 711-727.

ISSN 1071-5797

DOI: https://doi.org/10.1016/j.ffa.2012.01.002

## Project information

Project title: |
Project's official title Project's id Konstruktive Methoden in der algebraischen Codierungstheorie für lineare Codes über endlichen Kettenringen WA-1666/4 |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

Delsarte showed that for any projective linear code over a finite field GF(pʳ) with two nonzero Hamming weights w₁ < w₂ there exist positive integers u and s such that w₁ = pˢu and w₂ = pˢ(u+1). Moreover, he showed that the additive group of such a code has a strongly regular Cayley graph. Here we show that for any regular projective linear code C over a finite Frobenius ring with two integral nonzero homogeneous weights w₁ < w₂ there is a positive integer d, a divisor of |C|, and positive integer u such that w₁ = du and w₂ = d(u+1). This gives a new proof of the known result that any such code yields a strongly regular graph. We apply these results to existence questions on two-weight codes.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | ring-linear code; homogeneous weight; weight distribution; two-weight code; character module; strongly regular graph; Cayley graph |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 20 Nov 2014 08:27 |

Last Modified: | 09 Sep 2022 09:10 |

URI: | https://eref.uni-bayreuth.de/id/eprint/3731 |