Title data
Feulner, Thomas:
Classification and nonexistence results for linear codes with prescribed minimum distances.
In: Designs, Codes and Cryptography.
Vol. 70
(2014)
Issue 12
.
 pp. 127138.
ISSN 09251022
DOI: https://doi.org/10.1007/s1062301297008
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
Starting from a linear [n,k,d]_q code with dual distance d⊥, we may construct an [n−d⊥, k−d⊥+1, ≥d]_q code with dual distance at least ceil(d⊥/q) using construction Y1. The inverse construction gives a rule for the classification of all [n,k,d]_q codes with dual distance d⊥ by adding d⊥ further columns to the parity check matrices of the smaller codes. Isomorph rejection is applied to guarantee a small search space for this iterative approach. Performing a complete search based on this observation, we are able to prove the nonexistence of linear codes for 16 open parameter sets [n,k,d]_q , q = 2, 3, 4, 5, 7, 8. These results imply 217 new upper bounds in the known tables for the minimum distance of linear codes and establish the exact value in 109 cases.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Keywords:  Classification; Code equivalence; Construction Y1; Linear code; Residual code; Semilinear isometry 
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:  22 Jan 2015 10:20 
Last Modified:  22 Jan 2015 10:20 
URI:  https://eref.unibayreuth.de/id/eprint/5856 