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, Reed–Solomon, Reed–Muller, Bose–Chaudhuri–Hochquenghem, Turbo, Golay, Goppa, low-density parity-check codes, and space–time codes. Error detecting codes can be optimised to detect burst errors, or random errors. Codes and acronyms Acronyms and abbreviations can be considered codes, and in a sense all languages and writing systems are codes for human thought. 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". Coupon Codes In marketing, coupon codes can be used for a financial discount or rebate when purchasing a product from an internet retailer. Coupon codes are also referred to as "promotional codes," "promotion codes," "discount codes," "key codes," "promo codes," "shopping codes," "voucher codes" or "source codes."[1] 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 (a Gödel number). References ^ The History of Coupons

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