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Divisible minimal codes

Title data

Kurz, Sascha:
Divisible minimal codes.
Bayreuth , 2023 . - 14 p.
DOI: https://doi.org/10.15495/EPub_UBT_00007346

Official URL: Volltext

Abstract in another language

Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a k-dimensional linear code over GF(q) is denoted by m(k,q). Here we determine m(7,2), m(8,2), and m(9,2), as well as full classifications of all codes attaining m(k,2) for k<=7 and those attaining m(9,2). For m(11,2) and m(12,2) we give improved upper bounds. It turns out that in many cases attaining extremal codes have the property that the weights of all codewords are divisible by some constant &\Delta;>1. So, here we study the minimum lengths of minimal codes where we additionally assume that the weights of the codewords are divisible by &\Delta;.

Further data

Item Type: Preprint, postprint
Keywords: minimal codes; divisible codes
Subject classification: Mathematics Subject Classification Code: 94B05 (51E23)
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: 09 Dec 2023 22:00
Last Modified: 11 Dec 2023 10:17
URI: https://eref.uni-bayreuth.de/id/eprint/88011