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Update on the extension of good linear codes

Title data

Kohnert, Axel:
Update on the extension of good linear codes.
In: Electronic Notes in Discrete Mathematics. Vol. 26 (1 September 2006) . - pp. 81-85.
ISSN 1571-0653
DOI: https://doi.org/10.1016/j.endm.2006.08.015

Abstract in another language

In this short note we state how we construct new good linear codes C over the finite field with q elements. We start with already good (= high minimum distance d for given length n and dimension k) codes which we got for example by our method [2,3,4,5]. The advantage of this method is that we explictly get the words of minimum weight d. We try to extend the generator matrix of C by adding
columns with the property that at least s of the letters added to the codewords are different from 0. Using this we know that the minimum distance of the extended code is d + s as long as the second smallest weight was ≥ d + s.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: finite projective geometry; coding theory; linear codes; minimum weight
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 15:04
Last Modified: 16 Sep 2016 09:42
URI: https://eref.uni-bayreuth.de/id/eprint/5797