Abstract
Coding theory is a practical branch of mathematics concerned with the reliable transmission of information over communication channels. It allows errors to be detected and corrected, which is essential when messages are transmitted through a noisy communication channel. The channel could be a telephone line, radio link or satellite link, and coding theory is applicable to mobile communications and satellite communications. It is also applicable to storing information on storage systems such as the compact disc.
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Notes
- 1.
Recall from Chap. 7 that ℤ/nℤ = ℤ n = {[a] n :0 £ a £ n − 1} = {[0] n , [1] n , …., [n − 1] n }.
- 2.
A finite division ring is actually a field (i.e. it is commutative under multiplication).
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© 2013 Springer-Verlag London
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O’Regan, G. (2013). Coding Theory. In: Mathematics in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-4534-9_9
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DOI: https://doi.org/10.1007/978-1-4471-4534-9_9
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