## Title data

Kiermaier, Michael ; Zwanzger, Johannes:

**A ℤ₄-linear code of high minimum Lee distance derived from a hyperoval.**

*In:* Advances in Mathematics of Communications.
Vol. 5
(2011)
Issue 2
.
- pp. 275-286.

ISSN 1930-5346

DOI: https://doi.org/10.3934/amc.2011.5.275

## 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

In this paper we present a new non-free ℤ₄-linear code of length 29 and size 128 whose minimum Lee distance is 28. Its Gray image is a nonlinear binary code with parameters (58,2⁷,28), having twice as many codewords as the biggest linear binary codes of equal length and minimum distance. The code also improves the known lower bound on the maximal size of binary block codes of length 58 and minimum distance 28.

Originally the code was found by a heuristic computer search. We give a geometric construction based on a hyperoval in the projective Hjelmslev plane over ℤ₄ which allows an easy computation of the symmetrized weight enumerator and the automorphism group. Furthermore, a generalization of this construction to all Galois rings of characteristic 4 is discussed.

## Further data

Item Type: | Article in a journal |
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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 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 13:10 |

Last Modified: | 02 Feb 2022 14:48 |

URI: | https://eref.uni-bayreuth.de/id/eprint/3734 |