## 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
- Constacyclic code
- Quasi-cyclic code
- Reversible code
- Error-correcting output code (ECOC)
- Quantum-inspired classical block code
- Small-distance block 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

- [1]
- J. H. van Lint, Introduction to Coding Theory (Springer Berlin Heidelberg, 1999) DOI
- [2]
- C. E. Shannon, “Probability of Error for Optimal Codes in a Gaussian Channel”, Bell System Technical Journal 38, 611 (1959) DOI
- [3]
- C. E. Shannon, R. G. Gallager, and E. R. Berlekamp, “Lower bounds to error probability for coding on discrete memoryless channels. I”, Information and Control 10, 65 (1967) DOI
- [4]
- Fano, Robert M. The transmission of information. Vol. 65. Cambridge, MA, USA: Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949.
- [5]
- 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