Editing Block code (section)

{{Short description|Family of error-correcting codes that encode data in blocks}}
{{More footnotes needed|date=February 2025}}

In [[coding theory]], '''block codes''' are a large and important family of [[Channel coding|error-correcting codes]] that encode data in blocks.
There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, [[mathematician]]s, and [[computer scientist]]s to study the limitations of ''all'' block codes in a unified way.
Such limitations often take the form of ''bounds'' that relate different parameters of the block code to each other, such as its rate and its ability to detect and correct errors.

Examples of block codes are [[Reed–Solomon code]]s, [[Hamming code]]s, [[Hadamard code]]s, [[Expander code]]s, [[Golay code (disambiguation)|Golay code]]s, [[Reed–Muller code]]s and [[Polar code (coding theory)|Polar code]]s. These examples also belong to the class of [[linear code]]s, and hence they are called '''linear block codes'''.  More particularly, these codes are known as algebraic block codes, or cyclic block codes, because they can be generated using Boolean polynomials.

Algebraic block codes are typically [[Soft-decision decoder|hard-decoded]] using algebraic decoders.{{Technical statement|date=May 2015}}

The term ''block code'' may also refer to any error-correcting code that acts on a block of <math>k</math> bits of input data to produce <math>n</math> bits of output data <math>(n,k)</math>. Consequently, the block coder is a ''memoryless'' device. Under this definition codes such as [[turbo code]]s, terminated convolutional codes and other iteratively decodable codes (turbo-like codes) would also be considered block codes. A non-terminated convolutional encoder would be an example of a non-block (unframed) code, which has ''memory'' and is instead classified as a ''tree code''.

This article deals with "algebraic block codes".