jmhbrown/irreducible_residue_tuples

Calculates the frequency of residue tuples in irreducible polynomials over various finite fields

Irreducible Residue Tuples

Calculates the frequency of residue tuples in irreducible polynomials over various finite fields

Installing and Running

This code was written for python3 and uses the sympy, optparse, json, and loggging packages.

Run the code like so -

python main.py --help

Multiple runs can be defined in a config file.

• coeff is an ordered list (smallest to largest) of the possible coefficients. It also defines the function field that the polynomials are over.
• num_terms is the number of terms per polynomial.
• modulus_poly is the polynomial that should be used to calculate residues. Defined either as a list of coefficents, largest degree first or as a string representation of the polynomial, e.g. x**2+x+1. Note that its domain is taken from coeff.
• tuple_length is the length of the tuples whose frequencies should be calculated in the residues of the polynomials.

Here's an example:

[
  {
    "tuple_length": 2,
    "modulus_poly": [1,1,1],
    "coeff": [0,1],
    "num_terms": 5
  },
  {
    "tuple_length": 2,
    "modulus_poly": "x**2+x+1",
    "coeff": [0,1],
    "num_terms": 6
  }
]

Known Issues

• only works with fields with prime order. So, coeff must be a list with prime length