## Description

A code intended to encode a piece, or block, of a data stream on a block of \(n\) symbols. Each symbol is taken from some fixed possibly infinite alphabet \(\Sigma\) [1; Ch. 3], which can include bits, Galois fields, rings, or real numbers.

The overall alphabet of the code is \(\Sigma^n\), and \(n\) is called the length of the code. In some cases, only a subset of \(\Sigma^n\) is available to use for constructing the code. 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

## Rate

## Decoding

## Parent

## Children

- Sphere packing
- Matrix-based code
- Constant-weight code
- Quasi-cyclic code
- Reversible code
- Universally optimal code
- Locally decodable code (LDC)
- Locally testable code (LTC)
- Convolutional code — Convolutional codes for infinite block size are block codes consisting of infinite blocks.
- Ring code

## Cousin

## References

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- [2]
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- R. Gallager, Information Theory and Reliable Communication (Springer Vienna, 1972) DOI
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- I. Csiszár and J. Körner, Information Theory (Cambridge University Press, 2011) DOI
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- S. Arimoto, “On the converse to the coding theorem for discrete memoryless channels (Corresp.)”, IEEE Transactions on Information Theory 19, 357 (1973) DOI
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- S. H. Hassani, K. Alishahi, and R. L. Urbanke, “Finite-Length Scaling for Polar Codes”, IEEE Transactions on Information Theory 60, 5875 (2014) DOI
- [14]
- N. Sourlas, “Spin-glass models as error-correcting codes”, Nature 339, 693 (1989) DOI

## Page edit log

- Victor V. Albert (2023-02-14) — most recent

## Cite as:

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