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The binary Golay code, G 23 is a perfect code. That is, the spheres of radius three around code words form a partition of the vector space. G 23 is a 12-dimensional subspace of the space F 23 2. The automorphism group of the perfect binary Golay code G 23 (meaning the subgroup of the group S 23 of permutations of the coordinates of F 23
Binary cycle. A binary cycle is a method for generating electrical power from geothermal resources and employs two separate fluid cycles, hence binary cycle. The primary cycle extracts the geothermal energy from the reservoir, and secondary cycle converts the heat into work to drive the generator and generate electricity. [1]
In coding theory, the dual code of a linear code. is the linear code defined by. where. is a scalar product. In linear algebra terms, the dual code is the annihilator of C with respect to the bilinear form . The dimension of C and its dual always add up to the length n : A generator matrix for the dual code is the parity-check matrix for the ...
Code page. In computing, a code page is a character encoding and as such it is a specific association of a set of printable characters and control characters with unique numbers. Typically each number represents the binary value in a single byte. (In some contexts these terms are used more precisely; see Character encoding § Terminology .)
From today's featured article. Hudson Volcano is a volcano in the rugged mountains of southern Chile. Lying in the Southern Volcanic Zone of the Andes, it was formed by the subduction of the oceanic Nazca Plate under the continental South American Plate. Hudson has the form of a 10-kilometre-wide (6-mile) volcanic caldera filled with ice.
Decoding methods. In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, such as a binary symmetric channel .
A Barker code or Barker sequence is a finite sequence of N values of +1 and −1, with the ideal autocorrelation property, such that the off-peak (non-cyclic) autocorrelation coefficients. are as small as possible: for all . [1] Only nine Barker sequences [6] are known, all of length N at most 13. [7] Barker 's 1953 paper asked for sequences ...
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]