A code is a rule for converting a piece of information Information, in its most restricted technical sense, is an ordered sequence of symbols. As a concept, however, information has many meanings. Moreover, the concept of information is closely related to notions of constraint, communication, control, form, instruction, knowledge, meaning, mental stimulus, pattern, perception, and representation (for example, a letter A letter is an element in an alphabetic system of writing, such as the Greek alphabet and its descendants. Each letter in the written language is usually associated with one phoneme in the spoken form of the language, word A word is the smallest free form in a language, in contrast to a morpheme, which is the smallest unit of meaning. A word may consist of only one morpheme (e.g. wolf), but a single morpheme may not be able to exist as a free form (e.g. the English plural morpheme -s), phrase In grammar, a phrase is a group of words functioning as a single unit in the syntax of a sentence, or gesture A gesture is a form of non-verbal communication in which visible bodily actions communicate particular messages, either in place of speech or together and in parallel with spoken words. Gestures include movement of the hands, face, or other parts of the body. Gestures differ from physical non-verbal communication that does not communicate specific) into another form or representation (one sign A sign is an entity which signifies another entity. A natural sign is an entity which bears a causal relation to the signified entity, as thunder is a sign of storm. A conventional sign signifies by agreement, as a full stop signifies the end of a sentence. into another sign), not necessarily of the same type.

In communications Communication is a process of transferring information from one entity to another. Communication processes are sign-mediated interactions between at least two agents which share a repertoire of signs and semiotic rules. Communication is commonly defined as "the imparting or interchange of thoughts, opinions, or information by speech, writing, and information processing Information processing is the change of information in any manner detectable by an observer. As such, it is a process which describes everything which happens (changes) in the universe, from the falling of a rock (a change in position) to the printing of a text file from a digital computer system. In the latter case, an information processor is, encoding is the process by which information from a source A source or sender is one of the basic concepts of communication and information processing. Sources are objects which encode message data and transmit the information, via a channel, to one or more observers 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 language is difficult or impossible. For example, semaphore, where the configuration of flags Semaphore Flags are a system for conveying information at a distance by means of visual signals with hand-held flags, rods, disks, paddles, or occasionally bare or gloved hands. Information is encoded by the position of the flags; it is read when the flag is in a fixed position. Semaphores were adopted and widely used in the maritime world in the held by a signaller or the arms of a semaphore tower A semaphore telegraph, optical telegraph, shutter telegraph chain, Chappe telegraph, or Napoleonic semaphore is a system of conveying information by means of visual signals, using towers with pivoting shutters, also known as blades or paddles. Information is encoded by the position of the mechanical elements; it is read when the shutter is in 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 information theory Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and communicating data. Since its inception it and computer science Computer science or computing science is the study of the theoretical foundations of information and computation, and of practical techniques for their implementation and application in computer systems. It is frequently described as the systematic study of algorithmic processes that create, describe, and transform information. Computer science, a code is usually considered as an algorithm In mathematics, computer science, and related subjects, an 'algorithm' is an effective method for solving a problem expressed as a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields which uniquely represents symbols from some source alphabet In computer science and mathematical logic, an alphabet is a, usually finite, set of symbols or letters, e.g. characters or digits. The most common alphabet is {0,1}, the binary alphabet. A finite string is a finite sequence of letters from an alphabet; for instance a binary string is a string drawn from the alphabet {0,1}. An infinite sequence of, 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 {a,b,c} and whose target alphabet is the set {0,1}. 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 A formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set from which these letters are taken is called the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar ; accordingly, words that belong to a formal language are sometimes called well-formed words (, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets In computer science and mathematical logic, an alphabet is a, usually finite, set of symbols or letters, e.g. characters or digits. The most common alphabet is {0,1}, the binary alphabet. A finite string is a finite sequence of letters from an alphabet; for instance a binary string is a string drawn from the alphabet {0,1}. An infinite sequence of, respectively. A code is a total function In mathematics, a partial function from X to Y is a function ƒ: X' → Y, where X' is a subset of X. It generalizes the concept of a function by not forcing f to map every element of X to an element of Y . If X' = X, then ƒ is called a total function and is equivalent to a function. Partial functions are often used when the exact domain, X' , is mapping each symbol from S to a sequence of symbols In computing, word is a term for the natural unit of data used by a particular computer design. A word is simply a fixed sized group of bits that are handled together by the system. The number of bits in a word is an important characteristic of a computer architecture over T, and the extension of M to a homomorphism In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures . The word homomorphism comes from the Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "shape" 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 code word In telecommunication, a code word is an element of a code. Each code word is a sequence of symbols assembled in accordance with the specific rules of the code and assigned a unique meaning . Code words are typically used for reasons of secrecy or brevity from some dictionary, and concatenation In computer programming, string concatenation is the operation of joining two character strings end to end. For example, the strings "snow" and "ball" may be concatenated to give "snowball". In many programming languages, string concatenation is a binary infix operator of such code words give us an encoded string. Variable-length codes are especially useful when clear text characters have different probabilities; see also entropy encoding In information theory an entropy encoding is a lossless data compression scheme that is independent of the specific characteristics of the medium.

A prefix code is a code with the "prefix property": there is no valid code word In telecommunication, a code word is an element of a code. Each code word is a sequence of symbols assembled in accordance with the specific rules of the code and assigned a unique meaning . Code words are typically used for reasons of secrecy or brevity in the system that is a prefix (start) of any other valid code word in the set. Huffman coding In computer science and information theory, Huffman coding is an entropy encoding algorithm used for lossless data compression. The term refers to the use of a variable-length code table for encoding a source symbol where the variable-length code table has been derived in a particular way based on the estimated probability of occurrence for each is the most known algorithm for deriving prefix codes, so prefix codes are also widely referred to as "Huffman codes", even when the code was not produced by a Huffman algorithm. Another examples are country calling codes This is a list of country calling codes defined by ITU-T recommendations E.123 and E.164, also called IDD or ISD (International Subscriber Dialling) codes, the country and publisher parts of ISBNs The International Standard Book Number is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, now Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W.H. Smith and others in 1966, and the Secondary Synchronization Codes used in the UMTS Universal Mobile Telecommunications System is one of the third-generation (3G) mobile telecommunications technologies, which is also being developed into a 4G technology. The first deployment of the UMTS is the release99 (R99) architecture. It is specified by 3GPP and is part of the global ITU IMT-2000 standard. The most common form of UMTS uses W- W-CDMA W-CDMA , UMTS-FDD, UTRA-FDD, or IMT-2000 CDMA Direct Spread is an air interface standard found in 3G mobile telecommunications networks. It is the basis of Japan's NTT DoCoMo's FOMA service and the most-commonly used member of the UMTS family and sometimes used as a synonym for UMTS. It utilizes the DS-CDMA channel access method and the FDD 3G Wireless Standard are prefix codes.

Kraft's inequality 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.

Block codes

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 error-correcting code, and works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include Hamming codes In telecommunication, a Hamming code is a linear error-correcting code named after its inventor, Richard Hamming. Hamming codes can detect up to two simultaneous bit errors, and correct single-bit errors; thus, reliable communication is possible when the Hamming distance between the transmitted and received bit patterns is less than or equal to, Reed–Solomon, Reed–Muller, Walsh-Hadamard, Bose–Chaudhuri–Hochquenghem In coding theory the BCH codes form a class of parameterised error-correcting codes which have been the subject of much academic attention in the last fifty years. BCH codes were invented in 1959 by Hocquenghem, and independently in 1960 by Bose and Ray-Chaudhuri . The acronym BCH comprises the initials of these inventors' names, Turbo In information theory, turbo codes are a class of high-performance forward error correction (FEC) codes developed in 1993, which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the channel noise at which reliable communication is still possible given a code rate. Turbo codes are finding use in (, Golay, Goppa, low-density parity-check codes In information theory, a low-density parity-check code is an error correcting code, a method of transmitting a message over a noisy transmission channel. While LDPC and other error correcting codes cannot guarantee perfect transmission, the probability of lost information can be made as small as desired. LDPC was the first code to allow data, and space–time codes. 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 characters In computer and machine-based telecommunications terminology, a character is a unit of information that roughly corresponds to a grapheme, grapheme-like unit, or symbol, such as in an alphabet or syllabary in the written form of a natural language, 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 telegraphers Telegraphy is the long-distance transmission of written messages without physical transport of letters. It is a compound term formed from the Greek words tele = far and graphein (γραφειν) = write. Radiotelegraphy or wireless telegraphy transmits messages using radio. Telegraphy includes recent forms of data transmission such as fax, email, 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."). Code words In telecommunication, a code word is an element of a code. Each code word is a sequence of symbols assembled in accordance with the specific rules of the code and assigned a unique meaning . Code words are typically used for reasons of secrecy or brevity were chosen for various reasons: length In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire thickness. Another example is FET transistors, in which the channel width may be larger than channel length, pronounceability, 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 Black Chamber The Black Chamber, otherwise known as MI-8 or Cipher Bureau, was the United States' first peacetime cryptanalytic organization, and a forerunner of the National Security Agency. The only prior codes and cypher organizations maintained by the US government had been some intermittent, and always abandoned, attempts by Armed Forces branches prior to run by Herbert Yardley 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 data compression In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits than an unencoded representation would use, through use of specific encoding schemes predates the computer era; an early example is the telegraph Telegraphy is the long-distance transmission of written messages without physical transport of letters. It is a compound term formed from the Greek words tele = far and graphein (γραφειν) = write. Radiotelegraphy or wireless telegraphy transmits messages using radio. Telegraphy includes recent forms of data transmission such as fax, email, Morse code Morse code is a method of transmitting textual information as a series of on-off tones, lights, or clicks that can be directly understood by a skilled listener or observer without special equipment. The International Morse Code encodes the Roman alphabet, the Arabic numerals and a small set of punctuation and procedural signals as standardized where more-frequently used characters have shorter representations. Techniques such as Huffman coding In computer science and information theory, Huffman coding is an entropy encoding algorithm used for lossless data compression. The term refers to the use of a variable-length code table for encoding a source symbol where the variable-length code table has been derived in a particular way based on the estimated probability of occurrence for each are now used by computer-based algorithms In mathematics, computer science, and related subjects, an 'algorithm' is an effective method for solving a problem expressed as a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields 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 ASCII The American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text. Most modern character-encoding schemes are based on ASCII, though they support many more characters than did ASCII. In one or another (somewhat compatible) version, it is used by nearly all personal computers A computer is a programmable machine that receives input, stores and manipulates data//information, and provides output in a useful format, terminals A computer terminal is an electronic or electromechanical hardware device that is used for entering data into, and displaying data from, a computer or a computing system. Early terminals were inexpensive devices but very slow compared to punched cards or paper tape for input, but as the technology improved and video displays were introduced,, printers In computing, a printer is a peripheral which produces a hard copy of documents stored in electronic form, usually on physical print media such as paper or transparencies. Many printers are primarily used as local peripherals, and are attached by a printer cable or, in most newer printers, a USB cable to a computer which serves as a document, and other communication equipment. It represents 128 characters with seven-bit binary numbers—that is, as a string of seven 1s and 0s. In ASCIIvcx 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 byte (usually referred as code pages), integer code point (Unicode) or a byte sequence (UTF-8).

Genetic code

Biological organisms contain genetic material that is used to control their function and development. This is the DNA, which contains units named genes that can produce proteins through a code (genetic code) in which a series of triplets of four possible nucleotides are translated into one of twenty possible amino acids.

Gödel code

In mathematics, a Gödel code was the basis for the proof of Gödel's incompleteness theorem. Here, the idea was to map mathematical notation to a natural number (using a Gödel numbering).

Other

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

In marketing, coupon 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 cornet 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, as the sign language for deaf people and braille for blind people, are based in movement or tactile codes.

Musical scores are the most common way to encode music.

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

Cryptography

In the history of cryptography, codes were once common for ensuring the confidentiality of communications, although ciphers are now used instead. See code (cryptography).

Secret codes 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:

• Encoding (in cognition) is a basic perceptual process of interpreting incoming stimuli; technically speaking, it is a complex, multi-stage process of converting relatively objective sensory input (e.g., light, sound) into subjectively meaningful experience.
• A content format is a specific encoding format for converting a specific type of data to information.
• Text encoding uses a markup language to tag the structure and other features of a text to facilitate processing by computers. (See also Text Encoding Initiative.)
• Semantics encoding of formal language A in formal language B is a method of representing all terms (e.g. programs or descriptions) of language A using language B.
• Electronic encoding transforms a signal into a code optimized for transmission or storage, generally done with a codec.
• Neural encoding is the way in which information is represented in neurons.
• Memory encoding is the process of converting sensations into memories.
• Television encoding: NTSC, PAL and SECAM

Other examples of decoding include:

• Digital-to-analog converter, the use of analog circuit for decoding operations
• Decoding (Computer Science)
• Decoding methods, methods in communication theory for decoding codewords sent over a noisy channel
• Digital signal processing, the study of signals in a digital representation and the processing methods of these signals
• Word decoding, the use of phonics to decipher print patterns and translate them into the sounds of language

Codes and acronyms

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

International Air Transport Association airport codes are three-letter codes used to designate airports and used for bag tags.

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 journalism to mean "end of story", and it is sometimes used in other contexts to signify "the end".

References

See also

• Asemic writing
• Equipment codes
• Semiotics
• Quantum error correction

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