from sage.all import *

# Initialization
n = 255
F = GF(n + 1, 'a', modulus='primitive')
R = PolynomialRing(F, 's')
k = 223
t = n - k
alpha = F.gen()
s = R.gen()
generator_poly = prod([s - alpha**j for j in range(1, t + 1)])

# Convert received bytes to polynomial
received_bytes = b'O\x04\xc0A\xd1\xceY\x05\xb44\xda\xf6\xe5F_V\xd1N\xf9\xc2\xe2\x01l\xc2\xbb\xf0w:\x01\x8bw\xaa\x00\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\xab\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x8b\x1d\x1e\x1f !"#$%&\'()*\xa3,-./0123456789C;<=>?@ABCDEFGH#JKLMNOPQRSTUVW\x03YZ[\\]^_`abcdef+hijklmnopqrstuKwxyz{|}~\x7f\x80\x81\x82\x83\x84\xab\x86\x87\x88\x89\x8a\x8b\x8c\x8d\x8e\x8f\x90\x91\x92\x93\x8b\x95\x96\x97\x98\x99\x9a\x9b\x9c\x9d\x9e\x9f\xa0\xa1\xa2\xb3\xa4\xa5\xa6\xa7\xa8\xa9\xaa\xab\xac\xad\xae\xaf\xb0\xb1\xb3\xb3\xb4\xb5\xb6\xb7\xb8\xb9\xba\xbb\xbc\xbd\xbe\xbf\xc0\xc1\xc2\xc3\xc4\xc5\xc6\xc7\xc8\xc9\xca\xcb\xcc\xcd\xce\xcf\xd0\xd1\xd2\xd3\xd4\xd5\xd6\xd7\xd8\xd9\xda\xdb\xdc\xdd\xde'
received_poly = R(list(received_bytes))

# Compute syndromes
syndromes = [received_poly(alpha**i) for i in range(1, t + 1)]

# Berlekamp-Massey algorithm
def berlekamp_massey(syndromes):
    L = R(1)  # Current error locator polynomial
    B = R(1)  # Previous version of L
    m = 1
    b = F(1)  # Coefficient used to adjust L
    for n in range(len(syndromes)):
        discrepancy = syndromes[n]
        for k in range(1, len(L.coefficients())):
            if n-k < 0:
                break
            discrepancy += L[k] * syndromes[n - k]

        if discrepancy != 0:
            T = L
            L = L - discrepancy * b * B.shift(m)
            if 2 * len(T.coefficients()) <= n + 1:
                B = T
                b = discrepancy.inverse()
                m = n + 1 - len(T.coefficients())
    return L

# Check for errors
if not all(syndrome == 0 for syndrome in syndromes):
    # Apply Berlekamp-Massey algorithm to find error locator polynomial
    L = berlekamp_massey(syndromes)
    
    # Find the roots of the error locator polynomial (Chien Search)
    error_locations = []
    for i in range(n):
        if L(alpha**i) == 0:
            error_locations.append(n - 1 - i)

    # Calculate error values using Forney's algorithm
    error_values = []
    for loc in error_locations:
        X = alpha**(-loc)
        Y = received_poly(X)
        Z = L.derivative()(X)
        error_value = Y * X * Z.inverse()
        error_values.append(error_value)
else:
    error_locations = []
    error_values = []

# Output the error locations and values
error_locations, error_values