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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00006857
URN to cite this document: urn:nbn:de:bvb:703-epub-6857-0

Title data

Kiermaier, Michael ; Kurz, Sascha:
Classification of Δ-divisible linear codes spanned by codewords of weight Δ.
Bayreuth , 2023 . - 12 S.

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Abstract

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
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
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 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
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-6857-0
Date Deposited: 16 Feb 2023 06:45
Last Modified: 16 Feb 2023 06:46
URI: https://epub.uni-bayreuth.de/id/eprint/6857

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