How does the program for decoding BCH using the BMA method work?

Question

Programming

I really urgently need help understanding this program. I do not understand how they work and why there are some pieces of code that are given after the program code.

h = comm.BCHEncoder('CodewordLength', 31, 'MessageLength', 21); %object zanimaushisa kodirovaniem
msg = [1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0]; %б®®ЎйҐ­ЁҐ ў Ї®«Ґ ѓ «г /Message in Galois array
obj = comm.BCHEncoder('CodewordLength', 31, 'MessageLength', 21);

c1 = step(obj, msg(1,:)'); %zakodirovannoe soobshenie
cbch = [c1].';

coded = cbch;

% parametri
m=5;
n=2^m-1; %dlina soobshenia
t=2;
k=2^m-1-m*t;

%Є®­бв ­вл, ЁбЇ®«м§гҐ¬лҐ ў  «Ј®аЁв¬Ґ/the constants used in the algorithm
alpha = gf(2, m);
zero = gf(0, m);
one = gf(1, m);

%since all zero is always a codeword, only have to specify the
%error/vruchnuu zabili oshibki
coded(1) = 0;
coded(2) = 1;

code=gf(coded, 1); %massiv polei galua

codev = code.x; %dlya drugih vichislenii perevodim v massiv|ot massiva polei galua k obichnoi matrice
reccode=gf(codev, m);

%ᮧ¤ Ґ¬,  «мд  ¬ ббЁўcreating alpha array
%note that syndrome should be in the order [s3, s2, s1, s0] v obratnom poradke
alpha_tb=gf(zeros(1, 2*t), m);
for i=1:2*t,
    alpha_tb(i)=alpha^(2*t-i+1);
end;

%ЈҐ­ҐаЁа㥬 бЁ­¤а®¬/syndrome generation
syndrome=gf(zeros(1, 2*t), m)
for i=1:n,
    syndrome=syndrome.*alpha_tb+reccode(i);
end;


%imba
lambda = gf([1, zeros(1, t)], m);
lambda0= lambda;
b=gf([0, 1, zeros(1, t)], m);
b2 = gf([0, 0, 1, zeros(1, t)], m);
k=0;
gamma = one;
delta = zero;
syndrome_array = gf(zeros(1, t+1), m);

for r=1:t,
    r1 = 2*t-2*r+2;
    r2 = min(r1+t, 2*t);
    num = r2-r1+1;
    syndrome_array(1: num) = syndrome(r1:r2);
    delta = syndrome_array*lambda';

    lambda0 = lambda;
    lambda = gamma*lambda-delta*b2(2:t+2);

    if((delta~= zero) && (k>=0))
        b2(3)=zero;
        b2(4:3+t) = lambda0(1:t);
        gamma = delta;
        k = -k;
    else
        b2(3:3+t) = b2(1:t+1);
        gamma = gamma;
        k=k+2;
    end
end;

%massiv v obratnom poradke, tak kak alfa massiv mi zapisivali v obratnom
inverse_tb = gf(zeros(1, t+1), m);
for i=1:t+1,
    inverse_tb(i) = alpha^(-i+1);
end;

%Ї®ЁбЄ —ЁҐ­ /chien's search
lambda_v = zero;
accu_tb=gf(ones(1, t+1), m);
for i=1:n,
    lambda_v=lambda*accu_tb';
    accu_tb = accu_tb.*inverse_tb;
    if(lambda_v==zero)
        error(1,n-i+1)=1;
    else
        error(1,n-i+1)=0;
    end
end

found = find(error(1,:)~=0)

disp(coded);

sz = size(found); %proidemsa po found
length = sz(2);
for i=1:length,
    if(coded(i)==0)
        coded(i) = 1;
    else
        coded(i) = 0;
    end
end

disp(coded);

hh = comm.BCHDecoder('CodewordLength', 31, 'MessageLength', 21); %decodiruem ispravlennoe
obj = comm.BCHDecoder('CodewordLength', 31, 'MessageLength', 21);

d1 = step(obj, coded(1,:)'); %informazia dljya vosstanovlenia dobavlaetsa
dbch = [d1].';
disp(dbch);

one)

code=gf(coded, 1); %massiv polei galua

codev = code.x; %dlya drugih vichislenii perevodim v massiv|ot massiva polei galua k obichnoi matrice
reccode=gf(codev, m);

2)

%ᮧ¤ Ґ¬,  «мд  ¬ ббЁўcreating alpha array
%note that syndrome should be in the order [s3, s2, s1, s0] v obratnom poradke
alpha_tb=gf(zeros(1, 2*t), m);
for i=1:2*t,
    alpha_tb(i)=alpha^(2*t-i+1);
end;

3)

%ЈҐ­ҐаЁа㥬 бЁ­¤а®¬/syndrome generation
syndrome=gf(zeros(1, 2*t), m)
for i=1:n,
    syndrome=syndrome.*alpha_tb+reccode(i);
end;

4)

%imba
lambda = gf([1, zeros(1, t)], m);
lambda0= lambda;
b=gf([0, 1, zeros(1, t)], m);
b2 = gf([0, 0, 1, zeros(1, t)], m);
k=0;
gamma = one;
delta = zero;
syndrome_array = gf(zeros(1, t+1), m);

for r=1:t,
    r1 = 2*t-2*r+2;
    r2 = min(r1+t, 2*t);
    num = r2-r1+1;
    syndrome_array(1: num) = syndrome(r1:r2);
    delta = syndrome_array*lambda';

    lambda0 = lambda;
    lambda = gamma*lambda-delta*b2(2:t+2);

    if((delta~= zero) && (k>=0))
        b2(3)=zero;
        b2(4:3+t) = lambda0(1:t);
        gamma = delta;
        k = -k;
    else
        b2(3:3+t) = b2(1:t+1);
        gamma = gamma;
        k=k+2;
    end
end;

5)

%massiv v obratnom poradke, tak kak alfa massiv mi zapisivali v obratnom
inverse_tb = gf(zeros(1, t+1), m);
for i=1:t+1,
    inverse_tb(i) = alpha^(-i+1);
end;

6)

%Ї®ЁбЄ —ЁҐ­ /chien's search
lambda_v = zero;
accu_tb=gf(ones(1, t+1), m);
for i=1:n,
    lambda_v=lambda*accu_tb';
    accu_tb = accu_tb.*inverse_tb;
    if(lambda_v==zero)
        error(1,n-i+1)=1;
    else
        error(1,n-i+1)=0;
    end
end