Title data
Kiermaier, Michael ; Wassermann, Alfred ; Zwanzger, Johannes:
New upper bounds on binary linear codes and a ℤ₄code with a betterthanlinear Gray image.
In: IEEE Transactions on Information Theory.
Vol. 62
(2016)
Issue 12
.
 pp. 67686771.
ISSN 00189448
DOI: https://doi.org/10.1109/TIT.2016.2612654
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft Studienstiftung des deutschen Volkes 
Abstract in another language
Using integer linear programming and tablelookups, we prove that there is no binary linear [1988, 12, 992] code. As a byproduct, the nonexistence 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 Z4linear code having a nonlinear binary Gray image with the parameters 1988, 212,992. By our result, the code K6* can be added to the small list of Z4codes 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; ringlinear 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 (Computer Algebra) 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:  02 Feb 2022 14:28 
URI:  https://eref.unibayreuth.de/id/eprint/36947 