Code: Difference between revisions

Revision as of 12:59, 4 March 2022

Revision as of 17:23, 1 August 2022

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=== Error-correcting codes ===

{{mainMain|Error detection and correction}}

{{seeSee also|Block code}}

Codes may also be used to represent data in a way more resistant to errors in transmission or storage. This so-called [[Error detection and correction|error-correcting code]] works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include [[Hamming code]]s, [[Reed–Solomon]], [[Reed–Muller code|Reed–Muller]], [[Walsh–Hadamard code|Walsh–Hadamard]], [[BCH code|Bose–Chaudhuri–Hochquenghem]], [[Turbo code|Turbo]], [[Binary Golay code|Golay]], [[Goppa code|Goppa]], [[low-density parity-check code]]s, and [[space–time code]]s.

Error detecting codes can be optimised to detect ''burst errors'', or ''random errors''.

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=== Character encodings ===

{{Main|Character encoding}}

Character encodings are representations of textual data. A given character encoding may be associated with a specific character set (the collection of characters which it can represent), though some character sets have multiple character encodings and vice versa. Character encodings may be broadly grouped according to the number of bytes required to represent a single character: there are single-byte encodings, [[Wide character|multibyte]] (also called wide) encodings, and [[Variable-width encoding|variable-width]] (also called variable-length) encodings. The earliest character encodings were single-byte, the best-known example of which is [[ASCII]]. ASCII remains in use today, for example in [[HTTP headers]]. However, single-byte encodings cannot model character sets with more than 256 characters. Scripts that require large character sets such as [[CJK characters|Chinese, Japanese and Korean]] must be represented with multibyte encodings. Early multibyte encodings were fixed-length, meaning that although each character was represented by more than one byte, all characters used the same number of bytes ("word length"), making them suitable for decoding with a lookup table. The final group, variable-width encodings, is a subset of multibyte encodings. These use more complex encoding and decoding logic to efficiently represent large character sets while keeping the representations of more commonly used characters shorter or maintaining backward compatibility properties. This group includes [[UTF-8]], an encoding of the [[Unicode]] character set; UTF-8 is the most common encoding of text media on the Internet.

=== Genetic code ===

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[[Biology|Biological]] organisms contain genetic material that is used to control their function and development. This is [[DNA]], which contains units named [[gene]]s from which [[messenger RNA]] is derived. This in turn produces [[protein]]s through a [[genetic code]] in which a series of triplets ([[codon]]s) of four possible [[nucleotides]] can be translated into one of twenty possible [[amino acid]]s. A sequence of codons results in a corresponding sequence of amino acids that form a protein molecule; a type of codon called a [[stop codon]] signals the end of the sequence.

=== 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]]).