Block code

In coding theory, block codes are a large and important family of 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, mathematicians, and computer scientists 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 codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, 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 hard-decoded using algebraic decoders.

The term block code may also refer to any error-correcting code that acts on a block of

k

{\displaystyle k}

bits of input data to produce

n

{\displaystyle n}

bits of output data

(

n

,

k

)

{\displaystyle (n,k)}

. Consequently, the block coder is a memoryless device.