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This is a consequence of the fact that a parity check matrix of is a generator matrix of the dual code. G is a matrix, while H is a () matrix. Equivalent codes. Codes C 1 and C 2 are equivalent (denoted C 1 ~ C 2) if one code can be obtained from the other via the following two transformations: arbitrarily permute the components, and
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 original code and vice versa. The dual of the dual code is always the original code.
Cheating in video games involves a video game player using various methods to create an advantage beyond normal gameplay, usually in order to make the game easier.Cheats may be activated from within the game itself (a cheat code implemented by the original game developers), or created by third-party software (a game trainer or debugger) or hardware (a cheat cartridge).
A generator matrix for the binary Golay code is I A, where I is the 12×12 identity matrix, and A is the complement of the adjacency matrix of the icosahedron. A convenient representation. It is convenient to use the "Miracle Octad Generator" format, with co-ordinates in an array of 4 rows, 6 columns. Addition is taking the symmetric difference.
Singleton bound. In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound. [1] proved by Joshi (1958) and even earlier by Komamiya (1953) .
Sicilian town Sambuca di Sicilia will be putting a batch of abandoned homes up for sale. - Simone Padovani/Awakening/Alamy Stock Photo
Linear code. In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types. [1] Linear codes allow for more efficient encoding and ...
Kinky Friedman, the satirical and often provocative musician, author and one-time politician, has died at the age of 79. “Kinky Friedman stepped on a rainbow at his beloved Echo Hill surrounded ...