at Google ScholarTitle data
Kurz, Sascha:
Lengths of divisible codes : the missing cases.
In: Designs, Codes and Cryptography.
Vol. 92
(2024)
.
- pp. 2367-2378.
ISSN 1573-7586
DOI: https://doi.org/10.1007/s10623-024-01398-7
Abstract in another language
A linear code C over GF(q) is called Delta-divisible if the Hamming weights wt(c) of all codewords c in C are divisible by Delta. The possible effective lengths of q^r-divisible codes have been completely characterized for each prime power q and each non-negative integer r. The study of Δ divisible codes was initiated by Harold Ward. If c divides Delta but is coprime to q, then each Delta-divisible code C over GF(q) is the c-fold repetition of a Δ/c-divisible code. Here we determine the possible effective lengths of p^r-divisible 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: | Article in a journal |
|---|---|
| Refereed: | Yes |
| 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 > Department of Mathematics > Chair Mathematical Economics |
| 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 Feb 2025 09:40 |
| Last Modified: | 19 Feb 2025 09:40 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/92429 |