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Classification and nonexistence results for linear codes with prescribed minimum distances

Title data

Feulner, Thomas:
Classification and nonexistence results for linear codes with prescribed minimum distances.
In: Designs, Codes and Cryptography. Vol. 70 (2014) Issue 1-2 . - pp. 127-138.
ISSN 0925-1022
DOI: https://doi.org/10.1007/s10623-012-9700-8

Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
No informationWA 1666/7-1

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.uni-bayreuth.de/id/eprint/5856