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⬣ LINKS ⬣
⬡ PATREON: https://www.patreon.com/anotherroof
⬡ CHANNEL: https://www.youtube.com/c/AnotherRoof
⬡ WEBSITE: https://anotherroof.top
⬡ SUBREDDIT: https://www.reddit.com/r/anotherroof
⬡ TWITCH: https://www.twitch.tv/anotherroof
⬣ ABOUT ⬣
The (extended) Golay code is a beautiful structure that has many practical uses and also rears its head in areas of pure mathematics. It makes for an efficient means of communicating across the vast distances in space, while also popping up in the study of sporadic simple groups.
⬣ TIMESTAMPS ⬣
00:00 - Introduction and Housekeeping
03:52 - ISBN Error Detection
07:00 - Hamming Codes, Error Correction, and Linearity
19:45 - Weight and Distance in Linear Codes
25:17 - Golay Code
43:38 - Connection to S(5,8,24)
49:03 - Outro
⬣ INVESTIGATORS ⬣
Nothing for you here. Sorry!
⬣ REFERENCES ⬣
[1] E. R. Berlekamp. Key Papers in the Development of Coding Theory. IEEE Press (1974).
[2] M. Golay. Notes on Digital Coding. Proc. IRE, vol 37, p657 (1949).
[3] T. M. Thompson. From Error-Correcting Codes through Sphere Packings to Simple Groups, The Carus Mathematical Monographs (#21), Mathematical Association of America, pp. 16–17 (1983).
⬣ CREDITS ⬣
Music by Danjel Zambo.
Brief excerpt from “Moon Men” by Jake Chudnow.
Image Credits
Elwyn Berlekamp
https://commons.wikimedia.org/wiki/File:Elwyn_R_Berlekamp_2005.jpg
Pager
https://commons.wikimedia.org/wiki/File:Motorolapager.jpg
Voyager 1
NASA Public Domain Image
Sporadic Groups
https://commons.wikimedia.org/wiki/File:SporadicGroups.svg
Sphere Packing
https://commons.wikimedia.org/wiki/File:Close-packed_spheres.jpg
LIBRARIAN
NetFlix (fair use)
Richard Hamming
http://cm.bell-labs.com/cm/cs/alumni/hamming/
Punched Card
https://commons.wikimedia.org/wiki/File:Used_Punchcard_(5151286161).jpg
Marcel J. E. Golay (mathematician), Public Domain
https://ethw.org/w/images/e/e2/M._J._E._Golay.jpg
Marcel Golay (astronomer), Public Domain
https://commons.wikimedia.org/wiki/File:Marcel_Golay_(Swiss_astronomer).jpg
Claude Shannon
https://commons.wikimedia.org/wiki/File:ClaudeShannon_MFO3807.jpg