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On the minimum number of minimal codewords

Title data

dela Cruz, Romar ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On the minimum number of minimal codewords.
In: Advances in Mathematics of Communications. Vol. 17 (2023) Issue 2 . - pp. 333-341.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2020130

Official URL: Volltext

Abstract in another language

We study the minimum number of minimal codewords in linear codes using techniques from projective geometry. Minimal codewords have been used in decoding algorithms and cryptographic protocols. First, we derive a new lower bound on the number of minimal codewords. Then we give a formula for the minimum number of minimal codewords of linear codes for certain lengths and dimensions. We also determine the exact value of the minimum for a range of values of the length and dimension. As an application, we completed a table of the minimum number of minimal codewords for codes of length up to . Finally, we discuss an extension of the geometric approach to minimal subcode supports.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Minimal codewords; linear codes; projective geometry; secret sharing; decoding
Subject classification: Mathematics Subject Classification Code: 94B05 94B27 (94A60 94B35)
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 Mathematical Economics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics
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: 19 Jan 2023 09:44
Last Modified: 10 Aug 2023 13:43
URI: https://eref.uni-bayreuth.de/id/eprint/73472