Titlebar

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

 

New upper bounds on binary linear codes and a ℤ₄-code with a better-than-linear Gray image

Title data

Kiermaier, Michael ; Wassermann, Alfred ; Zwanzger, Johannes:
New upper bounds on binary linear codes and a ℤ₄-code with a better-than-linear Gray image.
In: IEEE Transactions on Information Theory. Vol. 62 (December 2016) Issue 12 . - pp. 6768-6771.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2016.2612654

Project information

Project title:
Project's official titleProject's id
No informationWA-1666/4

Project financing: Deutsche Forschungsgemeinschaft
Studienstiftung des deutschen Volkes

Abstract in another language

Using integer linear programming and table-lookups, we prove that there is no binary linear [1988, 12, 992] code. As a by-product, the non-existence of binary linear codes with the parameters [324, 10, 160], [356, 10, 176], [772, 11, 384], and [836, 11, 416] is shown. Our work is motivated by the recent construction of the extended dualized Kerdock code K6*, which is a Z4-linear code having a non-linear binary Gray image with the parameters 1988, 212,992. By our result, the code K6* can be added to the small list of Z4-codes for which it is known that the Gray image is better than any binary linear code.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: integer linear programming; linear codes; ring-linear codes; Kerdock codes
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 May 2017 11:11
Last Modified: 20 Feb 2018 06:08
URI: https://eref.uni-bayreuth.de/id/eprint/36947