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Divisible codes

Appears in collection : ALCOCRYPT - ALgebraic and combinatorial methods for COding and CRYPTography

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.

Information about the video

Date of recording 2/20/23
Date of publication 3/8/23
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.20006403
Cite this video Kurz Sascha (2/20/23). Divisible codes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20006403
URL https://dx.doi.org/10.24350/CIRM.V.20006403

Domain(s)

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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