# Hamming Encoder

Create Hamming code from binary vector data

## Library

Block sublibrary of Error Detection and Correction

## Description

The Hamming Encoder block creates a Hamming code with message length K and codeword length N. The number N must have the form 2M-1, where M is an integer greater than or equal to 3. Then K equals N-M.

This block accepts a column vector input signal of length K. The output signal is a column vector of length N.

The coding scheme uses elements of the finite field GF(2M). You can either specify the primitive polynomial that the algorithm should use, or you can rely on the default setting:

• To use the default primitive polynomial, simply enter N and K as the first and second dialog parameters, respectively. The algorithm uses `gfprimdf(M)` as the primitive polynomial for GF(2M).

• To specify the primitive polynomial, enter N as the first parameter and a binary vector as the second parameter. The vector represents the primitive polynomial by listing its coefficients in order of ascending exponents. You can create primitive polynomials using the Communications Toolbox™ `gfprimfd` function.

• In addition, you can specify the primitive polynomial as a character vector, for example, `'D^3 + D + 1'`.

For information about the data types each block port supports, see the Supported Data Type table on this page.

## Parameters

Codeword length N

The codeword length, which is also the output vector length.

Message length K, or M-degree primitive polynomial

The message length, which is also the input vector length or a binary vector that represents a primitive polynomial for GF(2M) or a polynomial character vector.

## Supported Data Type

PortSupported Data Types
In
• Double-precision floating point

• Single-precision floating point

• Boolean

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

• Fixed-point

Out
• Double-precision floating point

• Single-precision floating point

• Boolean

• 8-, 16-, and 32-bit signed integers

• 8-, 16-, and 32-bit unsigned integers

• Fixed-point

Hamming Decoder

## Version History

Introduced before R2006a