## Title data

Kiermaier, Michael ; Wassermann, Alfred:

**On the minimum Lee distance of quadratic residue codes over ℤ₄.**

*In:*
2008 IEEE International Symposium on Information Theory proceedings. -
Piscataway, NJ
: Institute of Electrical and Electronics Engineers (IEEE)
,
2008
. - pp. 2617-2619

ISBN 978-1-4244-2256-2

DOI: https://doi.org/10.1109/ISIT.2008.4595465

## 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

The class of the quadratic residue codes (QR-codes) over the ring ℤ₄ contains very good ℤ₄-linear codes. It is well known that the Gray images of the QR-codes over ℤ₄ of length 8, 32 and 48 are non-linear binary codes of higher minimum Hamming distance than comparable known linear codes. The QR-Code of length 48 is also the largest one whose exact minimum Lee distance was known. We developed a fast algorithm to compute the minimum Lee distance of QR-codes over ℤ₄, and applied it to all ℤ₄-linear QR-codes up to length 98. The QR-code of length 80 has minimum Lee distance 26. Thus it is a new example of a ℤ₄-linear code which is better than any known comparable linear code.

## Further data

Item Type: | Article in a book |
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Refereed: | Yes |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics 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: | 25 Nov 2014 15:21 |

Last Modified: | 25 Nov 2014 15:21 |

URI: | https://eref.uni-bayreuth.de/id/eprint/3901 |