How can I use additive secret sharing to share the secret key of BFV scheme among $N$ participants?

I want to share the secret key of the BFV scheme among N users using the additive secret-sharing protocol (n-out-of-n threshold secret-sharing). Can anyone please help me to adapt the two algorithms correctly?

Note that the secret key of BFV is generated as a random ternary polynomial from R 2 ( R 2 is the key distribution used to sample polynomials with integer coefficients in $\{-1,0,1\}$)

secret key generation algorithm (python code)

import numpy as np

def gen_binary_poly(size):
    """ Generates a polynomial with coeffecients in [0, 1]
    Args:
        size: number of coeffcients, size-1 being the degree of the polynomial.
    Returns:
        array of coefficients with the coeff[i] being the coeff of x ^ i.
    """
    return np.random.randint(0, 2, size, dtype=np.int64)


if __name__ == "__main__":
    
#polynomial modulus degree
size= 2**4  
secret_key = gen_binary_poly(size) 

additive secret sharing algorithm (code python)

import random

def getAdditiveShares(secret, N, fieldSize):
    '''Generate N additive shares from 'secret' in finite field of size 'fieldSize'.'''

    # Generate n-1 shares randomly
    shares = [random.randrange(fieldSize) for i in range(N-1)]

    # Append final share by subtracting all shares from secret
    # Modulo is done with fieldSize to ensure share is within finite field
    shares.append((secret - sum(shares)) % fieldSize )
    return shares

def reconstructSecret(shares, fieldSize):
    '''Regenerate secret from additive shares'''
    return sum(shares) % fieldSize

if __name__ == "__main__":

        N=5 # 5 users
    # Generating the shares
    shares = getAdditiveShares(secret, N, fieldSize)
    print('Shares are:', shares)
    
    # Reconstructing the secret from shares
    print('Reconstructed secret:', reconstructSecret(shares, fieldSize))