{{{id=1|
string = 'WORT'
num = map(lambda x: ord(x) - 64,string)
print num
///
[23, 15, 18, 20]
}}}

{{{id=2|
def digit(string):
    return map(lambda x: ord(x) - 64, string)
///
}}}

{{{id=3|
digit('WORT')
///
[23, 15, 18, 20]
}}}

{{{id=4|
def letters(num_list):
    return ''.join(chr(i+64) for i in num_list)
///
}}}

{{{id=5|
num = digit('WORT'); print num
letters(num)
///
[23, 15, 18, 20]
'WORT'
}}}

{{{id=6|
def reed_solomon(wort):
    liste = digit(wort)
    #a,b = var('a,b')
    a1 = (-sum( [ (k+2)*liste[k] for k in range(len(liste)) ] ))%31
    a0 = (-sum( [a1]+liste ))%31
    return letters([a0,a1] + liste)
///
}}}

{{{id=7|
reed_solomon('WORT')
///
'APWORT'
}}}

{{{id=8|
string = 'APWIRT'
liste = digit(string); liste
///
[1, 16, 23, 9, 18, 20]
}}}

{{{id=9|
e = sum(liste)%31; e
///
25
}}}

{{{id=10|
s = sum( [ k*liste[k] for k in range(len(liste)) ] )%31;s
///
13
}}}

{{{id=11|
x = s*power_mod(e,-1,31)%31; x
///
3
}}}

{{{id=21|
liste[x] = (liste[x]-e)%31;liste
///
}}}

{{{id=13|
def reed_solomon_inv(wort):
    liste = digit(wort)
    e = sum( liste )%31
    if e != 0:
        s = sum( [ k*liste[k] for k in range(len(liste)) ] )%31
        x = s*power_mod(e,-1,31)%31
        liste[x] = (liste[x] - e)%31
    liste = liste[2:]
    return letters( liste )
///
}}}

{{{id=14|
reed_solomon_inv('APWIRT')
///
'WORT'
}}}

{{{id=15|
code = reed_solomon('MATHEMATIK'); code
///
'JMMATHEMATIK'
}}}

{{{id=16|
code = code[:6]+'S'+code[7:];code
///
'JMMATHSMATIK'
}}}

{{{id=17|
reed_solomon_inv( code )
///
'MATHEMATIK'
}}}

{{{id=18|
code = code[:-1]+'J';code
///
'JMMATHSMATIJ'
}}}

{{{id=19|
reed_solomon_inv( code )
///
'MATHSMSTIJ'
}}}

{{{id=20|

///
}}}