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BINARY GOLAY-CODE

Binary Golay code

Type of linear error-correcting code

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,

Binary Golay code

Binary_Golay_code

Golay code

Topics referred to by the same term

Golay code may refer to: Binary Golay code, an error-correcting code used in digital communications Ternary Golay code (Golay) complementary sequences

Golay code

Golay_code

Leech lattice

24-dimensional repeating pattern of points

The binary Golay code, independently developed in 1949, is an application in coding theory. More specifically, it is an error-correcting code capable

Leech lattice

Leech_lattice

Mathieu group M24

Sporadic simple group

24 objects. (In coding theory the term "binary Golay code" often refers to a shorter related length 23 code, and the length 24 code used here is called

Mathieu group M24

Mathieu_group_M24

Ternary Golay code

Pair of related error-correcting codes

In coding theory, the ternary Golay codes are two closely related error-correcting codes. The code generally known simply as the ternary Golay code is

Ternary Golay code

Ternary_Golay_code

Error correction code

Scheme for controlling errors in data over noisy communication channels

GPS etc. Berger code Constant-weight code Convolutional code Expander codes Group codes Golay codes, of which the Binary Golay code is of practical interest

Error correction code

Error_correction_code

Miracle Octad Generator

Mathematical tool

tool introduced by Rob T. Curtis for studying the Mathieu groups, binary Golay code and Leech lattice. The Miracle Octad Generator is a 4x6 array of combinations

Miracle Octad Generator

Miracle_Octad_Generator

23 (number)

Natural number

vectors in the Leech lattice. The extended binary Golay code is an extension of the perfect binary Golay code B 23 {\displaystyle \mathbb {B} _{23}} , which

23 (number)

23_(number)

Golay

Topics referred to by the same term

Golay: Golay cell, a detector for infrared spectroscopy Savitzky–Golay filter, a signal processing filter Binary Golay code, an error-correcting code

Golay

24 (number)

Natural number

number 24 also occurs in coding theory and finite group theory through the extended binary Golay code, a self-dual binary linear code with parameters [ 24

24 (number)

24_(number)

POCSAG

Communications protocol

and adoption of the POCSAG code, pagers used one of several codes such as binary Golay code. In the 1990s new paging codes were developed that offered

POCSAG

Steiner system

Block design in combinatorial mathematics

the 24-bit binary Golay code are generated, and the 759 codewords with a Hamming weight of 8 correspond to the S(5,8,24) system. The Golay code can be constructed

Steiner system

Steiner_system

Mathieu group

Five sporadic simple groups

The group M24 is the permutation automorphism group of the extended binary Golay code W, i.e., the group of permutations on the 24 coordinates that map

Mathieu group

Mathieu_group

Low-density parity-check code

Linear error correcting code

Gilbert–Varshamov bound for linear codes over binary fields with high probability. Over the binary erasure channel, code sequences were designed at rates

Low-density parity-check code

Low-density_parity-check_code

Coding theory

Study of the properties of codes and their fitness

inventing the field of information theory. The binary Golay code was developed in 1949. It is an error-correcting code capable of correcting up to three errors

Coding theory

Coding_theory

Block code

Family of error-correcting codes that encode data in blocks

codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they

Block code

Block_code

Reed–Solomon error correction

Error-correcting codes

Reed–Solomon code is usually a poor choice compared to a binary code. The Reed–Solomon code, like the convolutional code, is a transparent code. This means

Reed–Solomon error correction

Reed–Solomon_error_correction

Even code

If the Hamming weight of all of a binary code's codewords is even

doubly even codes are the extended binary Hamming code of block length 8 and the extended binary Golay code of block length 24. These two codes are, in addition

Even code

Even_code

Cyclic code

Type of block code

n} . Multi-twisted codes are further generalizations of QT codes, which join multiple QT codes end to end. BCH code Binary Golay code Cyclic redundancy

Cyclic code

Cyclic_code

Turbo code

High-performance forward error correction codes

Elke; Papke, Luiz (March 1996). "Iterative Decoding of Binary Block and Convolutional Codes" (PDF). IEEE Transactions on Information Theory. 42 (2):

Turbo code

Turbo_code

Exceptional object

The codewords of the extended binary Golay code have a length of 24 bits and have weights 0, 8, 12, 16, or 24. This code can correct up to three errors

Exceptional object

Exceptional_object

Hamming code

Family of linear error-correcting codes

Hamming(7,4) code which adds three parity bits to four bits of data. In mathematical terms, Hamming codes are a class of binary linear codes. For each integer

Hamming code

Hamming_code

Conway group

Four finite groups derived from the Leech lattice

of Co0 with a subgroup he called N, a holomorph of the (extended) binary Golay code (as diagonal matrices with 1 or −1 as diagonal elements) by the Mathieu

Conway group

Conway_group

Quadratic residue code

{\displaystyle (23,12)} binary Golay code over G F ( 2 ) {\displaystyle GF(2)} and the ( 11 , 6 ) {\displaystyle (11,6)} ternary Golay code over G F ( 3 ) {\displaystyle

Quadratic residue code

Quadratic_residue_code

Barker code

Sequence of digital values used for synchronisation

Barker sequences or Barker codes, after the inventor Ronald Hugh Barker. The process is described in "Group Synchronisation of Binary Digital Systems" published

Barker code

Barker_code

Lexicographic code

Conway and Neil Sloane. The binary lexicographic codes are linear codes, and include the Hamming codes and the binary Golay codes. A lexicode of length n

Lexicographic code

Lexicographic_code

Linear code

Class of error-correcting code

linear code is a sequence of dual Hamming codes. Some examples of linear codes include: Repetition code Parity code Cyclic code Hamming code Golay code, both

Linear code

Linear_code

Distributed temperature sensing

Optoelectronic temperature sensing device

Code Correlation DTS sends on/off sequences of limited length into the fiber. The codes are chosen to have suitable properties, e.g. binary Golay code

Distributed temperature sensing

Distributed_temperature_sensing

M17 (amateur radio)

Open source amateur radio mode

(half-rate) modes. Three methods are used for error control: binary Golay code, punctured convolutional code and bit interleaving. Additionally, exclusive OR operation

M17 (amateur radio)

M17_(amateur_radio)

Sphere packing

Geometrical structure

linear codes. There are other, subtler relationships between Euclidean sphere packing and error-correcting codes. For example, the binary Golay code is closely

Sphere packing

Sphere_packing

Complementary sequences

Pairs of sequences

coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949. In 1961–1962 Golay gave several methods for

Complementary sequences

Complementary_sequences

Marcel J. E. Golay

Swiss mathematician (1902–1989)

Discoverer of the famous binary and ternary Golay codes, which are perfect error-correcting codes that generalize the Hamming code. They were used in the

Marcel J. E. Golay

Marcel_J._E._Golay

Rudin–Shapiro sequence

Rudin–Shapiro sequence, also known as the Golay–Rudin–Shapiro sequence, is an infinite 2-automatic sequence named after Marcel Golay, Harold S. Shapiro, and Walter

Rudin–Shapiro sequence

Rudin–Shapiro_sequence

List of algebraic coding theory topics

algorithm Binary Golay code Binary Goppa code Bipolar violation CRHF Casting out nines Check digit Chien's search Chipkill Cksum Coding gain Coding theory Constant-weight

List of algebraic coding theory topics

List_of_algebraic_coding_theory_topics

List of eponyms (A–K)

List of terms created from a person's name

scientist – Goethian, Goethite Marcel J.E. Golay, Swiss mathematician – Binary Golay code, Savitzky–Golay filter Rube Goldberg, American comics artist

List of eponyms (A–K)

List_of_eponyms_(A–K)

Concatenated error correction code

In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived

Concatenated error correction code

Concatenated_error_correction_code

Essentially unique

can be corrected, the solution is essentially unique: the extended binary Golay code. Classification theorem Modulo, a mathematical term pertaining to

Essentially unique

Essentially_unique

Moufang loop

Algebraic structure

is an elementary abelian group of order 212, identified with the binary Golay code. The loop is then defined up to isomorphism by the equations A2 =

Moufang loop

Moufang_loop

Janko group J4

Sporadic simple group

relation, certain products of commuting involutions generate the binary Golay code, which extends to the maximal subgroup 211:M24. Bolt, Bray, and Curtis

Janko group J4

Janko_group_J4

Capacitor

Electronic component

storage in capacitors to construct dynamic digital memories for the first binary computers that used electron tubes for logic. Pulsed power is used in many

Capacitor

Ternary

Topics referred to by the same term

heap, a data structure in computer science Ternary Golay code, a perfect [11, 6, 5] ternary linear code ?:, a ternary conditional operator used for basic

Ternary

Introduction to the Theory of Error-Correcting Codes

Book

the binary Golay codes, and the ternary Golay codes. The second edition adds material on BCH codes, Reed–Solomon error correction, Reed–Muller codes, decoding

Introduction to the Theory of Error-Correcting Codes

Introduction_to_the_Theory_of_Error-Correcting_Codes

Complementary code keying

Barker code, however, only has a single chipping sequence. The complementary codes first discussed by Golay were pairs of binary complementary codes and

Complementary code keying

Complementary_code_keying

Near polygon

Concept in incidence geometry

extended binary Golay code. It is constructed by taking the 759 octads (blocks) in the Witt design S(5, 8, 24) corresponding to the Golay code as points

Near polygon

Near_polygon

Local regression

Moving average and polynomial regression method for smoothing data

meta-model. In some fields, LOESS is known and commonly referred to as Savitzky–Golay filter (proposed 15 years before LOESS). LOESS and LOWESS thus build on

Local regression

Local_regression

Numerical differentiation

Use of numerical analysis to estimate derivatives of functions

methods for determining the weight coefficients, for example, the Savitzky–Golay filter. Differential quadrature is used to solve partial differential equations

Numerical differentiation

Numerical_differentiation

Central processing unit

Central computer component that executes instructions

representations such as bi-quinary coded decimal (base 2–5) or ternary (base 3). Nearly all modern CPUs represent numbers in binary form, with each digit being

Central processing unit

Central_processing_unit

Digital electronics

Electronic circuits that utilize digital signals

devices that use or produce them. It deals with the relationship between binary inputs and outputs by passing electrical signals through logical gates,

Digital electronics

Digital_electronics

Field-programmable gate array

Array of logic gates that are reprogrammable

validation techniques. Once the design and validation process is complete, the binary file generated, typically using the FPGA vendor's proprietary software,

Field-programmable gate array

Field-programmable_gate_array

Cathode ray tube

Vacuum tube used to display images

Williams-Kilburn tube was a cathode ray tube used to electronically store binary data. It was used in computers of the 1940s as a random-access digital storage

Cathode ray tube

Cathode_ray_tube

List of statistics articles

distribution – redirects to Luby transform code Somers' D Sørensen similarity index Spaghetti plot Sparse binary polynomial hashing Sparse PCA – sparse principal

List of statistics articles

List_of_statistics_articles

Beam deflection tube

Vacuum tube with an electron beam deflectable to one of two anodes

anode collected or passed the beam, producing current variations in binary code, one bit at a time. CK1414 Character generator monoscope for text mode

Beam deflection tube

Beam_deflection_tube

AI search references containing BINARY GOLAY-CODE

BINARY GOLAY-CODE

Golan

Girl/Female

Biblical

Golan

Passage, revolution.

Golan

HILARY

Male

English

HILARY

English unisex form of Latin Hilarius and Hilaria, HILARY means "joyful; happy."Â Originally, this was strictly a masculine name.

HILARY

Golan

Biblical

Golan

passage; revolution

Golan

EINAR

Male

Scandinavian

EINAR

Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."

EINAR

Binay

Boy/Male

Indian, Punjabi, Sikh

Binay

Blessing

Binay

Gola

Girl/Female

Hindu, Indian

Gola

A River

Gola

Golly

Surname or Lastname

English (Cornwall)

Golly

English (Cornwall) : variant of Gulley.German : variant of Gohl, or in the south of Goll.

Golly

Hilary

Boy/Male

American, Australian, French, German, Greek, Latin, Polish, Swedish

Hilary

Cheerful; Happy; Joyful; Similar to Hilary

Hilary

Binney

Surname or Lastname

English (chiefly South Yorkshire)

Binney

English (chiefly South Yorkshire) : topographic name for someone who lived on land enclosed by a bend in a river, from Old English binnan Ä“a â€˜within the riverâ€™, or a habitational name from places in Kent called Binney and Binny, which have this origin.Scottish : habitational name from Binney or Binniehill near Falkirk, named in Gaelic as Beinnach, from beinn â€˜hillâ€™ + the locative suffix -ach.

Binney