how to use a variable in finite field

sym a;

I want y=gf(3,8)*a, but it did not work.

[Manikanta Aditya]

% Create a Galois field array
g = gf(3, 8);
disp('Galois field array:');

Galois field array:

disp(g);

  gf with properties:

            x: 3
            m: 8
    prim_poly: 285

% Multiply the Galois field array by an integer
y = g * 2;
disp('Result after multiplication:');

Result after multiplication:

disp(y);

  gf with properties:

            x: 6
            m: 8
    prim_poly: 285

[ling]

Thank you! y=g*2, where 2 is a constant. Indeed, I require that y=g*a, where a is variable.

In my recent research, I need to reconstruct a polynomial using Lagrange interpolation in Galois field. During reconstruction, x is a variable and it is not incompatible with gf. Thus, I do know how to reconstruct a polynomial using Lagrange interpolation in Galois field.

[ling]

The polynomial can be easily reconstructed using Lagrange interpolation in GF(p),where p is a primer.

[Manikanta Aditya]

Yeah

Answer 1

[John D'Errico]

g = gf(3, 8)

 
g = GF(2^8) array. Primitive polynomial = D^8+D^4+D^3+D^2+1 (285 decimal)
 
Array elements = 
 
   3

whos g

  Name      Size            Bytes  Class    Attributes

  g         1x1                92  gf                 

g is a gf object. But g is not compatible for multiplication by a symbolic parameter. These are two independent (and unfortunately, incompatible) toolboxes. They don't talk to or with each other. This is why when you do try to multiply g with a symbolic object, it fails.

syms a
g*a

Error using gf
Expected input x to be one of these types:

double, single, uint8, uint16, uint32, uint64, int8, int16, int32, int64

Instead its type was sym.

Error in gf (line 191)
validateattributes(x,{'numeric'}, {'integer', ...

Error in gf>areCompatible (line 1481)
if ~isa(b,'gf'), b=gf(b,a.m,a.prim_poly); return; end

Error in * (line 931)
[x,y]=areCompatible(x,y,'mtimes');

As the error message says, the only things you can multiply a gf object by are in that list of numeric classes. A sym is not one of the allowed classes for that operation.

You could possibly write your own set of tools that would work as you wish, essentially rewriting the gf class. Since a sym can take on any value, and it MUST be discrete for that operation to make any sense at all, it might take some work on your part to do so in a valid way.

Answer 2

[Paul]

How about something along these lines?

y = @(a) gf(3,8)*a;
y(1)

 
ans = GF(2^8) array. Primitive polynomial = D^8+D^4+D^3+D^2+1 (285 decimal)
 
Array elements = 
 
   3

y(2)

 
ans = GF(2^8) array. Primitive polynomial = D^8+D^4+D^3+D^2+1 (285 decimal)
 
Array elements = 
 
   6