gen2par

Convert between parity-check and generator matrices

Syntax

`parmat = gen2par(genmat) genmat = gen2par(parmat) `

Description

`parmat = gen2par(genmat) ` converts the standard-form binary generator matrix `genmat` into the corresponding parity-check matrix `parmat`.

`genmat = gen2par(parmat) ` converts the standard-form binary parity-check matrix `parmat` into the corresponding generator matrix `genmat`.

The standard forms of the generator and parity-check matrices for an [n,k] binary linear block code are shown in the table below

Type of MatrixStandard FormDimensions
Generator [Ik P] or [P Ik] k-by-n
Parity-check [-P`'` In-k] or [In-k -P`'` ] (n-k)-by-n

.

where Ik is the identity matrix of size k and the `'` symbol indicates matrix transpose. Two standard forms are listed for each type, because different authors use different conventions. For binary codes, the minus signs in the parity-check form listed above are irrelevant; that is, -1 = 1 in the binary field.

Examples

The commands below convert the parity-check matrix for a Hamming code into the corresponding generator matrix and back again.

```parmat = hammgen(3) genmat1 = gen2par(parmat) parmat2 = gen2par(genmat1) % Ans should be the same as parmat above```

The output is

```parmat = 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 genmat = 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 parmat2 = 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 ```