## Title data

Kohnert, Axel:

**Update on the extension of good linear codes.**

*In:* Electronic Notes in Discrete Mathematics.
Vol. 26
(1 September 2006)
.
- pp. 81-85.

ISSN 1571-0653

DOI: https://doi.org/10.1016/j.endm.2006.08.015

## Abstract in another language

In this short note we state how we construct new good linear codes C over the finite field with q elements. We start with already good (= high minimum distance d for given length n and dimension k) codes which we got for example by our method [2,3,4,5]. The advantage of this method is that we explictly get the words of minimum weight d. We try to extend the generator matrix of C by adding

columns with the property that at least s of the letters added to the codewords are different from 0. Using this we know that the minimum distance of the extended code is d + s as long as the second smallest weight was ≥ d + s.

## Further data

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

Refereed: | Yes |

Keywords: | finite projective geometry; coding theory; linear codes; minimum weight |

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: | 22 Jan 2015 15:04 |

Last Modified: | 16 Sep 2016 09:42 |

URI: | https://eref.uni-bayreuth.de/id/eprint/5797 |