Isomorphism of Linear Codes

[Oleksandr Kazymyrov]

Hi all,

I have next code for checking CCZ-equivalence of two vectorial Boolean functions in magma:

n:=7;
GF:= FiniteField(2,n);
a:=PrimitiveElement(GF);

// returns the linear Code with columns (1,x,f(x))
function CF(f)
M:=Matrix( 2*n+1, 2^n, [1: x in GF] cat [Trace(a^i * x): x in GF, i in [1..n]] cat [Trace(a^i * f(x)): x in GF, i in [1..n]]);
return LinearCode( M );
end function;

f:=func<x | x^3 >;

g:=func<x | x^5 >;

if IsIsomorphic(CF(f),CF(g)) eq false
then "f and g are NOT equivalent";
else "f and g are equivalent" ;
end if;

I can't find analogue of IsIsomorphic in sage.It is the main problem of converting code to sage. Is sage has similar function? Or how to implement it?

Best regards,
Oleksandr

[David Joyner]

Do you want something like the LinearCode method is_permutation_equivalent?

>
> Best regards,
> Oleksandr
>
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[Oleksandr Kazymyrov]

It seems to be true. But are your sure that functions are equivalent?

On Thursday, June 7, 2012 5:05:11 PM UTC+2, David Joyner wrote:

On Thu, Jun 7, 2012 at 10:13 AM, Oleksandr Kazymyrov

> sage-support+unsubscribe@googlegroups.com

[Benjamin Jones]

It's conventional to define two linear codes to be isomorphic (or equivalent) if there is a permutation of the underlying basis which sends one code to the other. This is what `is_permutation_equivalent` checks. To be sure that this is the same, you should check the documentation for IsIsomorphic in magma. 

--

Benjamin Jones

[Oleksandr Kazymyrov]

Yeah, what I need. Thanks for the explanation.