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Additive codes attaining the Griesmer bound

Title data

Kurz, Sascha:
Additive codes attaining the Griesmer bound.
Bayreuth , 2025 . - I, 179 p.
DOI: https://doi.org/10.15495/EPub_UBT_00008788

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Official URL: Volltext

Abstract in another language

Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive codes can always be attained with equality if the minimum distance is sufficiently large. This solves the problem for the optimal parameters of additive codes when the minimum distance is large and yields many infinite series
of additive codes that outperform linear codes.

Further data

Item Type: Preprint, postprint
Keywords: additive codes; linear codes; Griesmer bound; Galois geometry
Subject classification: Mathematics Subject Classification Code: 05B25 94B65 (94B60)
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 Mathematical Economics
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: 22 Dec 2025 11:34
Last Modified: 22 Dec 2025 11:35
URI: https://eref.uni-bayreuth.de/id/eprint/95511

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