// General Hamming parity-check code (length 2^m - 1)
// Source: HeytingLean.CodingTheory.Hamming.General

use crate::hamming_basic::Bit;

pub fn hamming_length(m: u32) -> usize {
    (1usize << m) - 1
}

pub fn hamming_syndrome(m: u32, x: &[Bit]) -> Vec<Bit> {
    let n = hamming_length(m);
    (0..m).map(|k| {
        let mut sum: Bit = 0;
        for i in 0..n {
            let bit_k = if ((i + 1) >> k) & 1 == 1 { 1u8 } else { 0u8 };
            sum = (sum + bit_k * x[i]) & 1;
        }
        sum
    }).collect()
}

pub fn hamming_code_member(m: u32, x: &[Bit]) -> bool {
    hamming_syndrome(m, x).iter().all(|&s| s == 0)
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::hamming74::hamming74_encode;

    #[test]
    fn test_hamming_length() {
        assert_eq!(hamming_length(3), 7);
        assert_eq!(hamming_length(4), 15);
    }

    #[test]
    fn test_h3_codeword_membership() {
        // Hamming(7,4) codewords should be in H(3)
        let m = [1, 0, 1, 0];
        let enc = hamming74_encode(&m);
        assert!(hamming_code_member(3, &enc));
    }
}