Binary Golay code
Error-correcting code used in digital communications
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has deep connection to the theory of finite sporadic groups in mathematics.
Nº Q1534522 ★
Common · Knowledge
Binary Golay code
Error-correcting code used in digital communications
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has deep connection to the theory of finite sporadic groups in mathematics.
From Wikipedia
In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications. The binary Golay code, along with the ternary Golay code, has deep connection to the theory of finite sporadic groups in mathematics. These codes are named in honor of Marcel J. E. Golay whose 1949 paper introducing them has been called, by E. R. Berlekamp, the "best single published page" in coding theory. There are two closely related binary Golay codes. The extended binary Golay code, G24 (sometimes just called the "Golay code" in finite group theory) encodes 12 bits of data in a 24-bit word in such a way that any 3-bit errors can be corrected or any 7-bit errors can be detected. The other, the perfect binary Golay code, G23, has codewords of length 23 and is obtained from the extended binary Golay code by deleting one coordinate position (conversely, the extended binary Golay code is obtained from the perfect binary Golay code by adding a parity bit). In standard coding notation, the codes have parameters [24, 12, 8] and [23, 12, 7], corresponding to the length of the codewords, the dimension of the code, and the minimum Hamming distance between two codewords, respectively.
Text: Wikipédia, CC BY-SA 4.0. · Image: Life of Riley (Public domain) ·
Related cards
-
B
Barker code
Mathematical number sequence
Nº Q808256 ★
Not listed
-
F
Fundamental theorem of Galois theory
Theorem that describes the structure of certain types of field extensions
Nº Q766522 ★
Not listed
-
B
Binary blob
Closed-source device driver published only as binary code
Nº Q763151 ★
Not listed
-
F
Finagle's law
Anything that can go wrong, will—at the worst possible moment
Nº Q1349727 ★★
Not listed
-
Electronic color code
Indicator for the values or ratings of electronic components, very commonly for resistors
Nº Q4988919 ★★
Not listed
-
Binary number
System that represents numeric values using two symbols; 0 or 1
Nº Q3913 ★★★★
Not listed
-
Binary-coded decimal
Class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight. Special bit patterns are sometimes used for a sign or for other indications
Nº Q276582 ★★★
Not listed
-
B
Binary data
Data whose unit can take on only two possible states, traditionally labeled as 0 and 1 in accordance with the binary numeral system and Boolean algebra.
Nº Q4913888 ★★
Not listed
-
Hamming(7,4)
Linear error-correcting code
Nº Q2322550 ★
Not listed
-
Zeckendorf's theorem
Theorem that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum doesn’t include any two consecutive Fibonacci numbers
Nº Q1188392 ★
Not listed
-
Montgomery's pair correlation conjecture
Mathematical conjecture stated by Hugh Montgomery
Nº Q6905620 ★
Not listed
-
G
G-code
Programming languages
Nº Q620464 ★★★
Not listed
-
N
Nélio José Nicolai
Brazilian electrotechnician (1940-2017)
Nº Q10338430 ★★
Not listed
-
Gödel's incompleteness theorems
Theorem that a wide class of logical systems cannot be both consistent and complete
Nº Q200787 ★★★★
Not listed
-
Iterated logarithm
Inverse function to a tower of powers
Nº Q2028293 ★
Not listed
-
I
Inverse Galois problem
Unsolved problem in mathematics
Nº Q2358071 ★★
Not listed
-
Bernstein–Vazirani algorithm
Quantum algorithm
Nº Q65053013 ★
Not listed
-
F
Fibonacci coding
Universal code
Nº Q2633 ★★
Not listed