AN codes

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AN codes are error-correcting code that are used in arithmetic applications. ^[1] Arithmetic codes were commonly used in computer processors to ensure the accuracy of its arithmetic operations when electronics were more unreliable. Arithmetic codes help the processor to detect when an error is made and correct it. Without these codes, processors would be unreliable since any errors would go undetected. AN codes are arithmetic codes that are named for the integers ${\displaystyle A}$ and ${\displaystyle N}$ that are used to encode and decode the codewords.

These codes differ from most other codes in that they use arithmetic weight to maximize the arithmetic distance between codewords as opposed to the hamming weight and hamming distance. The arithmetic distance between two words is a measure of the number of errors made while computing an arithmetic operation. Using the arithmetic distance is necessary since one error in an arithmetic operation can cause a large hamming distance between the received answer and the correct answer.