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Classification of Δ-divisible linear codes spanned by codewords of weight Δ

Title data

Kiermaier, Michael ; Kurz, Sascha:
Classification of Δ-divisible linear codes spanned by codewords of weight Δ.
Bayreuth , 2021 . - 12 p.
DOI: https://doi.org/10.15495/EPub_UBT_00005227

Official URL: Volltext

Abstract in another language

We classify all q-ary Δ-divisible linear codes which are spanned by codewords of weight Δ. The basic building blocks are the simplex codes, and for q=2 additionally the first order Reed-Muller codes and the parity check codes. This generalizes a result of Pless and Sloane, where the binary self-orthogonal codes spanned by codewords of weight 4 have been classified, which is the case q=2 and Δ=4 of our classification. As an application, we give an alternative proof of a theorem of Liu on binary Δ-divisible codes of length 4Δ in the projective case.

Further data

Item Type: Preprint, postprint
Keywords: linear codes; divisible codes; classification
Subject classification: Mathematics Subject Classification Code: 94B05
Institutions of the University: 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 II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau
Faculties
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Date Deposited: 23 Jan 2021 22:00
Last Modified: 25 Jan 2021 07:38
URI: https://eref.uni-bayreuth.de/id/eprint/62349