README

Accompanying repository to the manuscript titled Weak Instances of the Two Matrix Code Equivalence Problem

Requirements

import sys
import argparse
from random import choice
import numpy as np
from time import time
    
# SageMath imports
from sage.all import (
    matrix,
    identity_matrix,
    zero_matrix,
    FiniteField,
    vector,
)

Instructions

% sage -python two_smce.py                       
usage: two_smce.py [-h] [-k CODE_DIMENSION] [-m CODE_LENGTH_M] -n CODE_LENGTH_N -q PRIME [-i]

Parses command.

options:
  -h, --help            show this help message and exit
  -k, --code_dimension CODE_DIMENSION
                        Code dimension parameter k
  -m, --code_length_m CODE_LENGTH_M
                        Code length parameter m
  -n, --code_length_n CODE_LENGTH_N
                        Code length parameter n
  -q, --prime PRIME     Field characteristic
  -i, --simce           For solving sIMCE instances

Solver can be tested as follows

# 2-sMCE
sage -python two_smce.py -q 4093 -k 20 -m 20 -n 20
sage -python two_smce.py -q 4093 -k 31 -m 31 -n 31
sage -python two_smce.py -q 2039 -k 42 -m 42 -n 42

# sIMCE
sage -python two_smce.py -q 4093 -k 20 -m 20 -n 20 --simce
sage -python two_smce.py -q 4093 -k 31 -m 31 -n 31 --simce
sage -python two_smce.py -q 2039 -k 42 -m 42 -n 42 --simce

Remarks

The code correctly runs on the SageMath version: SageMath version 10.8, Release Date: 2025-12-18.

License

Apache License Version 2.0, January 2004