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Divisible codes
Multi angle
Authors : Kurz, Sascha (Author of the conference)
CIRM (Publisher )
05B25 - Finite geometries, See also {51D20, 51Exx}
51E23 - Spreads and packing problems
94B05 - Linear codes, general
CIRM (Publisher )
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Abstract :
A linear code over Fq with the Hamming metric is called ∆-divisible if the weights of all codewords are divisible by ∆. They have been introduced by Harold Ward a few decades ago. Applications include subspace codes, partial spreads, vector space partitions, and distance optimal codes. The determination of the possible lengths of projective divisible codes is an interesting and comprehensive challenge.
Keywords : divisible codes; partial spreads; vector space partitions; subspace codes; finite geometry
MSC Codes : Keywords : divisible codes; partial spreads; vector space partitions; subspace codes; finite geometry
05B25 - Finite geometries, See also {51D20, 51Exx}
51E23 - Spreads and packing problems
94B05 - Linear codes, general
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Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 08/03/2023 Conference Date : 20/02/2023 Subseries : Research talks arXiv category : Combinatorics ; Information Theory Mathematical Area(s) : Combinatorics ; Computer Science Format : MP4 (.mp4) - HD Video Time : 01:04:17 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-02-20_kurz.mp4 
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Information on the Event
Event Title : ALCOCRYPTEvent Organizers : Bonnecaze, Alexis ; Mesnager, Sihem ; Solé, Patrick Dates : 20/02/2023 - 24/02/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2804.html
Citation Data
DOI : 10.24350/CIRM.V.20006403Cite this video as: Kurz, Sascha (2023). Divisible codes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20006403 URI : http://dx.doi.org/10.24350/CIRM.V.20006403 |
See Also
- [Multi angle] Almost there: capacity of private information retrieval from coded and colluding servers / Author of the conference Hollanti, Camilla.
- [Multi angle] Projective Reed Muller codes revisited / Author of the conference Ghorpade, Sudhir.
- [Multi angle] On APN and AB power functions / Author of the conference Budaghyan, Lilya.
Bibliography
- KURZ, Sascha. Divisible codes. arXiv preprint arXiv:2112.11763, 2021. - https://doi.org/10.48550/arXiv.2112.11763
- KIERMAIER, Michael et KURZ, Sascha. On the lengths of divisible codes. IEEE Transactions on Information Theory, 2020, vol. 66, no 7, p. 4051-4060. - https://doi.org/10.1109/TIT.2020.2968832
- HONOLD, Thomas, KIERMAIER, Michael, et KURZ, Sascha. Partial spreads and vector space partitions. Springer International Publishing, 2018. - http://dx.doi.org/10.1007/978-3-319-70293-3_7
- HONOLD, Thomas, KIERMAIER, Michael, KURZ, Sascha, et al. The lengths of projective triply-even binary codes. IEEE Transactions on Information Theory, 2019, vol. 66, no 5, p. 2713-2716. - https://doi.org/10.1109/TIT.2019.2940967
- KURZ, Sascha et MATTHEUS, Sam. A generalization of the cylinder conjecture for divisible codes. IEEE Transactions on Information Theory, 2021, vol. 68, no 4, p. 2281-2289. - https://doi.org/10.1109/TIT.2021.3134201
- BOUYUKLIEV, Iliya, BOUYUKLIEVA, Stefka, et KURZ, Sascha. Computer classification of linear codes. IEEE Transactions on Information Theory, 2021, vol. 67, no 12, p. 7807-7814. - https://doi.org/10.1109/TIT.2021.3114280
- KURZ, Sascha. No projective 16-divisible binary linear code of length 131 exists. IEEE Communications Letters, 2020, vol. 25, no 1, p. 38-40. - https://doi.org/10.1109/LCOMM.2020.3021939
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