[RS]利用matlab生成rs编码的生成多项式

function [genpoly,t] = rsgenpoly(N, K, varargin)
%RSGENPOLY Generator polynomial of Reed-Solomon code.
% GENPOLY = RSGENPOLY(N,K) returns the narrow-sense generator polynomial of a
% Reed-Solomon code with codeword length N and message length K. The codeword
% length N must have the form 2^m-1 for some integer m between 3 and 16. The
% output GENPOLY is a Galois row vector that represents the coefficients of

% the generator polynomial in order of descending powers. The narrow-sense
% generator polynomial is (X-alpha)*(X-alpha^2)*...*(X-alpha^(N-K)), where
% alpha is a root of the default primitive polynomial for the field GF(N+1).
%
% GENPOLY = RSGENPOLY(N,K,PRIM_POLY) is the same as the syntax above, except
% that PRIM_POLY specifies the primitive polynomial for GF(N+1) that has alpha
% as a root. PRIM_POLY is an integer whose binary representation indicates
% the coefficients of the primitive polynomial in order of descending powers.
% To use the default primitive polynomial, set PRIM_POLY to [].
%
% GENPOLY = RSGENPOLY(N,K,PRIM_POLY,B) returns the generator polynomial
% (X-alpha^B)*(X-alpha^(B+1))*...*(X-alpha^(B+N-K-1)), where B is an integer
% and alpha is a root of PRIM_POLY.
%
% [GENPOLY,T] = RSGENPOLY(...) returns T, the error-correction capability of
% the code.
%
% Examples:
% g = rsgenpoly(7,3) % Narrow-sense generator polynomial
% g2 = rsgenpoly(7,3,13) % Narrow-sense generator polynomial,
% % with respect to primitive polynomial
% % D^3+D^2+1
% g3 = rsgenpoly(7,3,[],4) % Use b=4
%
% See also GF, RSENC, RSDEC.



% Copyright 1996-2007 The MathWorks, Inc.
% $Revision: 1.4.4.2 $ $Date: 2007/09/14 15:57:43 $


% Initial checks
error(nargchk(2,4,nargin,'struct'));

% Number of optional input arguments
nvarargin = nargin - 2;

% Error-correcting capability
t = floor((N-K)/2);
t2 = N-K;
m = log2(N+1);
def_primpoly = 1;
b = 1; % Default : narrow-sense

if any([~isscalar(N) | ~isscalar(K) | floor(N)~=N | floor(K)~=K])
error('comm:rsgenpoly:InvalidNK','N and K must be positive scalar integers.');
end

if t2<1
error('comm:rsgenpoly:NLessThanK','N must be larger than K.');
end

if m~=floor(m) | m<3 | m>16
error('comm:rsgenpoly:InvalidN','N must equal 2^m-1 for some integer m between 3 and 16.')
end

if ~isempty(varargin)

prim_poly = varargin{1};

% Check prim_poly
if isempty(prim_poly)
if ~isnumeric(prim_poly)
error('comm:rsgenpoly:InvalidDefaultPrim_Poly','To use the default PRIM_POLY, it must be marked by [].');
end
else
if ~isscalar(prim_poly)
error('comm:rsgenpoly:Prim_PolyNotScalar','PRIM_POLY must be a scalar integer.');
end
% ZZZ add isprimitive once it's available
def_primpoly = 0;
end

if nvarargin==2
b = varargin{2};
if ~isscalar(b) | floor(b)~=b
error('comm:rsgenpoly:BNotAnInt','B must be an integer scalar.');
end
end
end

% Alpha is the primitive element of this GF(2^m) field
if def_primpoly == 1
alpha = gf(2,m);
else
alpha = gf(2,m,prim_poly);
end


genpoly = 1;
for k=mod(b+[0:t2-1],N)
 evalc('genpoly = conv(genpoly,[1 alpha.^(k)]);');
end


只需要在函数的末尾加上

genpoly=genpoly.x;

运行的结果：
>> pp=rsgenpoly(31,25)

pp =

1 17 26 30 27 30 24

该函数是matlab自带的函数，简单处理了一下输出结果类型，找了好久才找到

http://www.chinavib.com/thread-97264-1-1.html

本文地址：http://114er.blogspot.com/2010/12/rsmatlabrs.html 原创文章如转载，请注明链接： 转自Welcome Funny Guys