Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

New ring-linear codes from dualization in projective Hjelmslev geometries

Title data

Kiermaier, Michael ; Zwanzger, Johannes:
New ring-linear codes from dualization in projective Hjelmslev geometries.
In: Designs, Codes and Cryptography. Vol. 66 (January 2013) Issue 1–3 . - pp. 39-55.
ISSN 0925-1022
DOI: https://doi.org/10.1007/s10623-012-9650-1

Project information

Project title:
Project's official titleProject'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 article, several new constructions for ring-linear codes are given. The class of base rings are the Galois rings of characteristic 4, which include ℤ₄ as its smallest and most important member. Associated with these rings are the Hjelmslev geometries, and the central tool for the construction is geometric dualization. Applying it to the ℤ₄-preimages of the Kerdock codes and a related family of codes we will call Teichmüller codes, we get two new infinite series of codes and compute their symmetrized weight enumerators. In some cases, residuals of the original code give further interesting codes. The generalized Gray map translates our codes into ordinary, generally non-linear codes in the Hamming space. The obtained parameters include (58, 2⁷, 28)₂, (60, 2⁸, 28)₂, (114, 2⁸, 56)₂, (372, 2¹⁰, 184)₂ and (1988, 2¹², 992)₂ which provably have higher minimum distance than any linear code of equal length and cardinality over an alphabet of the same size (better-than-linear, BTL), as well as (180, 2⁹, 88)₂, (244, 2⁹, 120)₂, (484, 2¹⁰, 240)₂ and (504, 4⁶, 376)₄ where no comparable (in the above sense) linear code is known (better-than-known-linear, BTKL).

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: ring-linear code; Kerdock code; Lee weight; homogeneous weight; Galois ring; Gray map; Hjelmslev geometry
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 08:00
Last Modified: 12 Feb 2015 09:34
URI: https://eref.uni-bayreuth.de/id/eprint/3727