# 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 polynomial character vector or a row vector that gives the coefficients of the generator polynomial in order of ascending powers.

## Examples

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Calculate the minimum distance of a cyclic code using several methods.

Create the generate polynomial for a (7,4) cyclic code.

```n = 7; genpoly = cyclpoly(n,4);```

Calculate the minimum distance for the cyclic code using:

1. Generator polynomial `genmat`

2. Parity check matrix `parmat`

3. Generator polynomial `genpoly`

4. Generator polynomial specified as a character vector

```[parmat, genmat] = cyclgen(n,genpoly); wts = [gfweight(genmat,'gen') gfweight(parmat,'par'),... gfweight(genpoly,n) gfweight('1+x2+x3',n)]```
```wts = 1×4 3 3 3 3 ```

## Version History

Introduced before R2006a