Title data
Kurz, Sascha:
Lengths of divisible codes  the missing cases.
Bayreuth
,
2024
.  12 p.
DOI: https://doi.org/10.15495/EPub_UBT_00007502
This is the latest version of this item.
Abstract in another language
A linear code C over GF(q) is called Δdivisible if the Hamming weights wt(c) of all codewords c in C are divisible by Δ. The possible effective lengths of q^rdivisible codes have been completely characterized for each prime power q and each nonnegative integer r. The study of Δ divisible codes was initiated by Harold Ward. If c divides Δ but is coprime to q, then each Δdivisible code C over GF(q) is the cfold repetition of a Δ/cdivisible code. Here we determine the possible effective lengths of p^rdivisible codes over finite fields of characteristic p, where r is an integer but p^r is not a power of the field size, i.e., the missing cases.
Further data
Item Type:  Preprint, postprint 

Keywords:  Divisible codes; linear codes; Galois geometry 
Subject classification:  Mathematics Subject Classification Code: 51E23 (05B40) 
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:  08 Mar 2024 07:28 
Last Modified:  08 Mar 2024 07:28 
URI:  https://eref.unibayreuth.de/id/eprint/88834 
Available Versions of this Item

Lengths of divisible codes  the missing cases. (deposited 11 Nov 2023 22:01)
 Lengths of divisible codes  the missing cases. (deposited 08 Mar 2024 07:28) [Currently Displayed]