Block code

Description

A code defined on a block of \(n\) symbols, with each symbol taken from some fixed possibly infinite alphabet \(\Sigma\) [1; Ch. 3]. Such alphabets include bits, Galois fields, rings, or real numbers, and the overall alphabet of the code is \(\Sigma^n\). In this context, \(n\) is called the length of the code. In some cases, there are conditions on which length-\(n\) strings are available to the codes. For example, in the case of spherical codes, one is constrained to \(n\)-dimensional real vectors on the unit sphere.

An alternative more stringent definition (not used here) is in terms of a map encoding logical information from \(\Sigma^k\) into \(\Sigma^n\), yielding an \((n,k,d)_{\Sigma}\) block code, where \(d\) is the code distance.

Protection

Block codes protect from errors acting on a few of the \(n\) symbols. A block code with distance \(d\) detects errors acting on up to \(d-1\) symbols, and corrects erasure errors on up to \(d-1\) symbols.

Parent

Children

Cousin

References

[1]
J. H. van Lint, Introduction to Coding Theory (Springer Berlin Heidelberg, 1999) DOI
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Zoo Code ID: block

Cite as:
“Block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/block
BibTeX:
@incollection{eczoo_block, title={Block code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/block} }
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https://errorcorrectionzoo.org/c/block

Cite as:

“Block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/block

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/properties/block/block.yml.