update include and using of modules - use only one of this options

[fepaul-book]

In the project are several modules with dependencies shown below
All modules export some functions, but when a module is used by another module most of the modules are not only imported by using the "using" statement but also "include" the module

using statement:
allows to access exported functions without module prefix e.g. encrypt
if a function is not exported you can only access it by module_name.function_name e.g. McEliece.encrypt
include statement:
makes content of this file available in current file - as if the code was written in this file - there exports and stuff like that does not
matter at all
--> using "include" and "using" on same file is bad practice and should be updated

Overview of dependancies

Misc [self-contained]
InvalidCodewordError, - defines new Exception called InvalidCodewordError
string2bits, - Takes a plaintext and returns its binary representation
- with as much padding as needed to make its length divisible by k.
bits2string - Returns the string that msg represents.

ExtensionField [self-contained]
primitivePolynomials, - dictionary of irreducible polynomials for given degree
add, - add polynomials
multiply, - in GF(2)
divide, - only quotient in GF(2) with extended Euclidean
modulo, - only remainder
power, - x^n modulo g in GF(2^m)
inverse, - of a mod g
squareroot, - of p in GF(2^m)
polygcd - of polynomials

FiniteFieldMatrix [ExtensionField Random Nemo LinearAlgebra]
multiplyPolyMatrices!, - Multiplies two matrices in GF(2^m)
gaussianEliminationColumnPivoting!, - Applies Gauss-Jordan elimination
- to matrix H of dimension nxk.
- It also permutes a given code support
- to keep a coherent goppa code.
GeneratorInverse!, - Finds the right inverse of a generator matrix.
getPermutation, - Returns a random permutation matrix of dimension nxn.
getScrambler - Returns a random binary non-singular matrix of dimension kxk.

Polynomials [ExtensionField]
PolynomialConstants, - defines 0, 1, x as polynomial
monomial, - Returns a monomial of the given degree.
evaluate!, - Evaluates p(x) modulo g(x).
addRing!, - Adds two polynomials with coefficients in GF(2^m).
multiplyRing!, - Multiplies two polynomials with coefficients in GF(2^m).
divRing!, - Returns the quotient of a/b with coefficients in GF(2^m).
modRing!, - Returns the remainder of a/b with coefficients in GF(2^m).
makePolynomialMonic!, - Returns p as a monic polynomial by dividing p by the
- inverse of its leading coefficient.
inverseRing!, - Computes the inverse of a mod g with coefficients in GF(2^m).
- Throws an exception if the inverse doesn't exist.
isPolynomialIrreducible!, - Checks if the given polynomial has at least one root in GF(2^m).
- TODO: is irreducible the right term here? i guess not
- Returns true if it doesn't have roots, false otherwise.
randomPoly, - Returns a random monic irreducible polynomial of degree t
- over the extension field GF(2^m).
splitPolynomial! - Splits the polynomial p into even and odd terms in GF(2^m).

Goppa [Misc ExtensionField FiniteFieldMatrix Polynomials StatsBase LinearAlgebra DelimitedFiles]
generateGoppaCode, - Generates a (n, k) irreducible linear Goppa code with minimum
- distance d >= 2t + 1. Returns the generator matrix G, the goppa
- polynomial, the code support, and the number of rows k of G.
- return G, goppaPolynomial, codeSupport, k
decode! - Given a msg with noise, finds a codeword in the goppa code defined
- by the goppaPolynomial and codeSupport in GF(2^m)

McEliece [Misc FiniteFieldMatrix GoppaCode Random StatsBase DelimitedFiles]
generateKeys,
saveKeys,
encrypt, - enc returns array of ciphertexts of length k
decrypt,
haltingCheck

Test [McEliece DelimitedFiles]