Golay G24

This is a dirty implemenation of Golay correcting code using python.

This is a solution to 18.13 problem 1 from Trappe and Washington’s Crytography book. To run this, you need bash, python, and the numpy libraries. To run, run golay.sh.  The algorithm is located in golay.py

golay.py

#!/usr/bin/env python
 
from numpy import *
import sys
 
geng24 = array([[1,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,1,0,0,0,1,0],
                [0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1],
                [0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,1,1,1,0,0,0],
                [0,0,0,1,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,1,1,1,0,0],
                [0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,1,1,1,0],
                [0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0,1,1,1],
                [0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,1,1,0,1,1],
                [0,0,0,0,0,0,0,1,0,0,0,0,1,1,1,0,0,0,1,0,1,1,0,1],
                [0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,0,0,1,0,1,1,0],
                [0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1],
                [0,0,0,0,0,0,0,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,1],
                [0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,1,1,1,1,1]])
 
B = array([[1,1,1,0,1,1,1,0,0,0,1,0],
           [1,0,1,1,0,1,1,1,0,0,0,1],
           [1,1,0,1,1,0,1,1,1,0,0,0],
           [1,0,1,0,1,1,0,1,1,1,0,0],
           [1,0,0,1,0,1,1,0,1,1,1,0],
           [1,0,0,0,1,0,1,1,0,1,1,1],
           [1,1,0,0,0,1,0,1,1,0,1,1],
           [1,1,1,0,0,0,1,0,1,1,0,1],
           [1,1,1,1,0,0,0,1,0,1,1,0],
           [1,0,1,1,1,0,0,0,1,0,1,1],
           [1,1,0,1,1,1,0,0,0,1,0,1],
           [0,1,1,1,1,1,1,1,1,1,1,1]])
 
errorvector = array([0,0,0,0,0,0,0,0,0,0,0,0])
 
def weight(obj):
  wt = 0
  for i in obj:
    wt += i
  return wt
 
geng24_transpose = geng24.transpose()
 
#r = array([1,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0])
#r = array([0,1,0,0,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1])
#r = array([0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0])
#r = array([1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1])
 
r = []
for i in sys.argv[1].split(','):
  r.append(int(i))
r = array(r)
 
s = (dot(r,geng24_transpose) % 2 )
 
sdotb = (dot(s,B) % 2 )
 
#e = array([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0])
e = zeros( (1,24), dtype=int8)
e = e.flat
 
if weight(s) <= 3:
  print "ERROR CORRECTION 3"
  e = array([s, array([0,0,0,0,0,0,0,0,0,0,0,0])])
  e.shape = (1,24)
  e = e.flat
 
if weight(sdotb) <= 3:
  print "ERROR CORRECTION 4"
  e_new = array([array([0,0,0,0,0,0,0,0,0,0,0,0]), sdotb])
  e_new.shape = (1,24)
  e = (e + e_new) % 2
  e = e.flat
 
for j in range(12,24):
  if weight((geng24[:,j] + s)%2) < 2:
    print "ERROR CORRECTION 5"
    e[j] = 1
    e_new = array([(geng24[:,j]+s)%2, array([0,0,0,0,0,0,0,0,0,0,0,0])])
    e_new.shape = (1,24)
    e = (e + e_new) % 2
    e = e.flat
 
for j in range(0,12):
  if weight((sdotb + B[j,:])%2) <= 2:
    print "ERROR CORRECTION 6"
    e[j] = 1
    e_new = array([array([0,0,0,0,0,0,0,0,0,0,0,0]),((sdotb + B[j,:])%2)])
    e_new.shape = (1, 24)
    e = (e + e_new) % 2
    e = e.flat
 
print "\ne =  [",
for i in e:
  print i,
print "]\n"
 
c = ((e + r)%2)
m = array(c[:12])
 
print "r = ", r
print "c = ", c
print "m = ", m

Here is golay.sh

#!/bin/bash
 
echo "Running with Example Problem"
echo "==========================="
./golay.py 1,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,1,0
 
echo "
Running with Problem1"
echo "==========================="
./golay.py 0,1,0,0,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1
 
echo "
Running with Problem2"
echo "==========================="
./golay.py 0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,0
 
echo "
Running with Problem3"
echo "==========================="
./golay.py 1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1

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