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

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