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Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words.
From this construction, RM(r,m) is a binary linear block code (n, k, d) with length n = 2 m, dimension (,) = (,) + (,) and minimum distance = for . The dual code to RM( r,m ) is RM( m - r -1, m ). This shows that repetition and SPC codes are duals, biorthogonal and extended Hamming codes are duals and that codes with k = n /2 are self-dual.
The Burrows–Wheeler transform (BWT, also called block-sorting compression) rearranges a character string into runs of similar characters. This is useful for compression, since it tends to be easy to compress a string that has runs of repeated characters by techniques such as move-to-front transform and run-length encoding.
Linear block codes are frequently denoted as [n, k, d] codes, where d refers to the code's minimum Hamming distance between any two code words. (The [n, k, d] notation should not be confused with the (n, M, d) notation used to denote a non-linear code of length n, size M (i.e., having M code words), and minimum Hamming distance d.)
For this particular example, the linear string corresponds to: 01234567 Q*-+abcd. which is the straightforward reading of the expression tree from top to bottom and from left to right. These linear strings are called k-expressions (from Karva notation). Going from k-expressions to expression trees is also very simple.
This LDPC code fragment represents a three-bit message encoded as six bits. Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code, with n = 6 and k = 3. Again ignoring lines going out of the picture, the parity-check matrix representing this graph fragment is
Schematic structure of an autoencoder with 3 fully connected hidden layers. The code (z, or h for reference in the text) is the most internal layer. Autoencoders are often trained with a single-layer encoder and a single-layer decoder, but using many-layered (deep) encoders and decoders offers many advantages. [2]
In the example above, the minimum Hamming distance is 2, since 01001 is a codeword, and there is no nonzero codeword with only one bit set. More specific properties of a polynomial code often depend on particular algebraic properties of its generator polynomial.