# gfweight

Calculate minimum distance of linear block code

## Syntax

`wt = gfweight(genmat)wt = gfweight(genmat,'gen')wt = gfweight(parmat,'par')wt = gfweight(genpoly,n)`

## Description

The minimum distance, or minimum weight, of a linear block code is defined as the smallest positive number of nonzero entries in any n-tuple that is a codeword.

`wt = gfweight(genmat)` returns the minimum distance of the linear block code whose generator matrix is `genmat`.

`wt = gfweight(genmat,'gen')` returns the minimum distance of the linear block code whose generator matrix is `genmat`.

`wt = gfweight(parmat,'par')` returns the minimum distance of the linear block code whose parity-check matrix is `parmat`.

`wt = gfweight(genpoly,n)` returns the minimum distance of the cyclic code whose codeword length is `n` and whose generator polynomial is represented by `genpoly`. `genpoly` is a row vector that gives the coefficients of the generator polynomial in order of ascending powers.

## Examples

The commands below illustrate three different ways to compute the minimum distance of a (7,4) cyclic code.

```n = 7; % Generator polynomial of (7,4) cyclic code genpoly = cyclpoly(n,4); [parmat, genmat] = cyclgen(n,genpoly); wts = [gfweight(genmat,'gen'),gfweight(parmat,'par'),... gfweight(genpoly,n)]```

The output is

```wts = 3 3 3 ```