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