URN to cite this document: urn:nbn:de:bvb:703-epub-7283-8
Title data
Kurz, Sascha:
Lengths of divisible codes - the missing cases.
Bayreuth
,
2023
. - 12 S.

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Abstract
A linear code C over GF(q) is called Δ-divisible if the Hamming weights wt(c) of all codewords c in C are divisible by Δ. 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 Δ but is coprime to q, then each Δ-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: | Preprint, postprint |
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Keywords: | Divisible codes; linear codes; Galois geometry |
Subject classification: | Mathematics Subject Classification Code: 51E23 (05B40) |
DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
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 |
Language: | English |
Originates at UBT: | Yes |
URN: | urn:nbn:de:bvb:703-epub-7283-8 |
Date Deposited: | 06 Nov 2023 06:58 |
Last Modified: | 06 Nov 2023 06:59 |
URI: | https://epub.uni-bayreuth.de/id/eprint/7283 |
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