The Golay code is thus an error-correcting code. It was originally published in with Marcel Golay’s half-page paper, “Notes on Digital Coding”. Today, this . Marcel Jules Edouard Golay was a Swiss-born mathematician, physicist, and information Golay, M. (). “Notes on Digital Coding” (PDF). Proc. IRE. Notes on Digital Coding – Marcel J. E. Golay () [pdf] (). 1 point by espeed 2 days ago | hide | past | web | favorite | discuss.
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When Voyager visited Saturn and Jupiter, data for the pictures used blocks of Golay code.
Each bit block of data could have up to three errors, and the computers here on Earth dlgital fix these errors. The Golay code is thus an error-correcting code. Today, this paper is considered one of the most remarkable papers ever published, with deep, deep connections to group theory, graph theory, number theory, combinatorics, game theory, multidimensional geometry, and even particle physics.
Marcel J. E. Golay – Wikipedia
The bit Golay code is called a perfect code. Any integer from 0 to is within distance three of one of the code words, so that up to three errors can notez detected and corrected.
The automorphism digitall is the Mathieu group The only other nontrivial perfect codes are the ternary Golay code and the Hamming code. The code words of weight 7 are elements of an 4, 7, 23 Steiner system. The bit Golay code is called a semiperfect code. Any integer from 0 to is within distance four of one of the code words.
Up to four golat can be detected and up to three errors can be corrected. The automorphism group is the Mathieu group The code words of weight eight are elements of an 5, 8, 24 Steiner system. Start a list with the bit 0 word … Add the first bit word that has eight or more differences from all words in the list.
Repeat, to get the code words. The code words are winning positions in the game of Mogul, played with 24 coins in a row.
Each turn flips between one and seven coins such that the leftmost flipped coin goes from heads to tails. Last to move wins.
These 12 vectors serve as a basis for the code words. If an integer is squared modulus 23, the result will not be inthe quadratic nonresidues mod In a bit code word, change those places to 1.
Obtain 11 more lists by adding 1 to 11 tomod Finally, change the bit of each to 1 and gain a basis for the code words. Modulus 2, one factor of is Consider the powers ofnamely. There are coing with seven terms.
Notes on Digital Coding – Marcel J. E. Golay () [pdf] | Hacker News
Choose 12 polynomial powers with differing initial terms, and append 1 to each polynomial’s coefficient list to obtain a basis for the code words. Golay, “Notes on Digital Coding,” Proc.
IRE37, p. Sloane, Sphere Packings, Cding, and Groups3rd ed. Ed Pegg Jr “Golay Code” http: Download free CDF Player. Details This Demonstration builds the Golay code in four different ways.