Theory
In information theory and computer science, a code is usually considered as an algorithm which uniquely represents symbols from some source alphabet, by encoded strings, which may be in some other target alphabet. An extension of the code for representing sequences of symbols over the source alphabet is obtained by concatenating the encoded strings.
Before giving a mathematically precise definition, we give a brief example. The mapping
is a code, whose source alphabet is the set and whose target alphabet is the set . Using the extension of the code, the encoded string 0011001011 can be grouped into codewords as 0 – 011 – 0 – 01 – 011, and these in turn can be decoded to the sequence of source symbols acabc.
Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively. A code is a total function mapping each symbol from S to a sequence of symbols over T, and the extension of M to a homomorphism of into, which naturally maps each sequence of source symbols to a sequence of target symbols, is referred to as its extension.
Read more about this topic: Code
Famous quotes containing the word theory:
“There is in him, hidden deep-down, a great instinctive artist, and hence the makings of an aristocrat. In his muddled way, held back by the manacles of his race and time, and his steps made uncertain by a guiding theory which too often eludes his own comprehension, he yet manages to produce works of unquestionable beauty and authority, and to interpret life in a manner that is poignant and illuminating.”
—H.L. (Henry Lewis)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)
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—Anna Quindlen (20th century)