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Code  ( Encodings )

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A code is a rule for converting a piece of (for example, a , , , or ) into another - usually or - form or representation (one into another sign), not necessarily of the same type.

In and , encoding is the process by which information from a is converted into symbols to be communicated. Decoding is the reverse process, converting these code symbols back into information understandable by a receiver.

One reason for coding is to enable communication in places where ordinary , spoken or written, is difficult or impossible. For example, semaphore, where the configuration of held by a signaller or the arms of a encodes parts of the message, typically individual letters and numbers. Another person standing a great distance away can interpret the flags and reproduce the words sent.

Theory
In and , a code is usually considered as an which uniquely represents symbols from some source , 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

$C = \\left\{\, a\mapsto 0, b\mapsto 01, c\mapsto 011\,\\right\}$
is a code, whose source alphabet is the set $\\left\{a,b,c\\right\}$ and whose target alphabet is the set $\\left\{0,1\\right\}$. 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 , the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target , respectively. A code $C:\, S \to T^*$ is a mapping each symbol from S to a over T, and the extension of $C$ to a of $S^*$ into $T^*$, which naturally maps each sequence of source symbols to a sequence of target symbols, is referred to as its extension.

Variable-length codes
In this section we consider codes, which encode each source (clear text) character by a from some dictionary, and of such code words give us an encoded string. Variable-length codes are especially useful when clear text characters have different probabilities; see also .

A prefix code is a code with the "prefix property": there is no valid in the system that is a (start) of any other valid code word in the set. is the most known algorithm for deriving prefix codes. Prefix codes are widely referred to as "Huffman codes", even when the code was not produced by a Huffman algorithm. Other examples of prefix codes are , the country and publisher parts of , and the Secondary Synchronization Codes used in the 3G Wireless Standard.

characterizes the sets of code word lengths that are possible in a prefix code. Virtually any uniquely decodable one-to-many code, not necessary a prefix one, must satisfy Kraft's inequality.

Error-correcting codes
Codes may also be used to represent data in a way more resistant to errors in transmission or storage. Such a "code" is called an , and works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include , , , , , , , , , and . Error detecting codes can be optimised to detect burst errors, or random errors.

Examples

Codes in communication used for brevity
A cable code replaces words (e.g., ship or invoice) with shorter words, allowing the same information to be sent with fewer , more quickly, and most important, less expensively.

Codes can be used for brevity. When telegraph messages were the state of the art in rapid long distance communication, elaborate systems of commercial codes that encoded complete phrases into single words (commonly five-letter groups) were developed, so that became conversant with such "words" as BYOXO ("Are you trying to weasel out of our deal?"), LIOUY ("Why do you not answer my question?"), BMULD ("You're a skunk!"), or AYYLU ("Not clearly coded, repeat more clearly."). were chosen for various reasons: , , etc. Meanings were chosen to fit perceived needs: commercial negotiations, military terms for military codes, diplomatic terms for diplomatic codes, any and all of the preceding for espionage codes. Codebooks and codebook publishers proliferated, including one run as a front for the American run by between the First and Second World Wars. The purpose of most of these codes was to save on cable costs. The use of data coding for predates the computer era; an early example is the where more-frequently used characters have shorter representations. Techniques such as are now used by computer-based to compress large data files into a more compact form for storage or transmission.

Character encodings
Probably the most widely known data communications code so far (aka character representation) in use today is . In one or another (somewhat compatible) version, it is used by nearly all personal , , , and other communication equipment. It represents 128 with seven-bit numbers—that is, as a string of seven 1s and 0s (). In ASCII a lowercase "a" is always 1100001, an uppercase "A" always 1000001, and so on. There are many other encodings, which represent each character by a (usually referred as ), integer () or a byte sequence ().

Genetic code
organisms contain genetic material that is used to control their function and development. This is which contains units named that can produce through a code () in which a series of triplets () of four possible are translated into one of twenty possible . A sequence of codons results in a corresponding sequence of amino acids that form a protein.

Gödel code
In , a was the basis for the proof of 's . Here, the idea was to map to a (using a ).

Other
There are codes using colors, like , the employed to mark the nominal value of the or that of the trashcans devoted to specific types of garbage (paper, glass, biological, etc.)

In , codes can be used for a financial discount or rebate when purchasing a product from an internet retailer.

In military environments, specific sounds with the are used for different uses: to mark some moments of the day, to command the infantry in the battlefield, etc.

Communication systems for sensory impairments, such as for deaf people and for blind people, are based on movement or tactile codes.

are the most common way to encode .

Specific games, as , have their own code systems to record the matches ().

Cryptography
In the , codes were once common for ensuring the confidentiality of communications, although are now used instead. See .

intended to obscure the real messages, ranging from serious (mainly espionage in military, diplomatic, business, etc.) to trivial (romance, games) can be any kind of imaginative encoding: flowers, game cards, clothes, fans, hats, melodies, birds, etc., in which the sole requisite is the previous agreement of the meaning by both the sender and the receiver.

Other examples
Other examples of encoding include:

Other examples of decoding include:

Codes and acronyms
and abbreviations can be considered codes, and in a sense all and writing systems are codes for human thought.

are three-letter codes used to designate airports and used for . are similarly used on railways, but are usually national, so the same code can be used for different stations if they are in different countries.

Occasionally a code word achieves an independent existence (and meaning) while the original equivalent phrase is forgotten or at least no longer has the precise meaning attributed to the code word. For example, '30' was widely used in to mean "end of story", and has been used in to signify "the end".Kogan, Hadass "So Why Not 29" American Journalism Review. Retrieved 2012-07-03.

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