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Lengths of divisible codes - the missing cases

Title data

Kurz, Sascha:
Lengths of divisible codes - the missing cases.
Bayreuth , 2024 . - 12 p.
DOI: https://doi.org/10.15495/EPub_UBT_00007502

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Official URL: Volltext

Abstract in another language

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
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.uni-bayreuth.de/id/eprint/88834

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