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

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 (May 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 titleProject's id
Konstruktive Methoden in der algebraischen Codierungstheorie für lineare Codes über endlichen KettenringenWA-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
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
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: 10 Dec 2014 12:24
URI: https://eref.uni-bayreuth.de/id/eprint/3734