Block code 


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.


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.


Ideal decoding error scales is suppressed exponentially with the number of subsystems \(n\), and the exponent has been studied in Ref. [24].


Decoding an error-correcting code is equivalent to finding the ground state of some statistical mechanical model [5].





J. H. van Lint, Introduction to Coding Theory (Springer Berlin Heidelberg, 1999) DOI
C. E. Shannon, “Probability of Error for Optimal Codes in a Gaussian Channel”, Bell System Technical Journal 38, 611 (1959) DOI
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
Fano, Robert M. The transmission of information. Vol. 65. Cambridge, MA, USA: Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949.
N. Sourlas, “Spin-glass models as error-correcting codes”, Nature 339, 693 (1989) DOI
Page edit log

Your contribution is welcome!

on (edit & pull request)— see instructions

edit on this site

Zoo Code ID: block

Cite as:
“Block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_block, title={Block code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:

Cite as:

“Block code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.