diff --git a/crates/melo-erasure-coding/src/erasure_coding.rs b/crates/melo-erasure-coding/src/erasure_coding.rs
index d0ac3d8..08d44bb 100644
--- a/crates/melo-erasure-coding/src/erasure_coding.rs
+++ b/crates/melo-erasure-coding/src/erasure_coding.rs
@@ -23,11 +23,37 @@ use rust_kzg_blst::{
 	utils::reverse_bit_order,
 };
 
+/// Extends the given `source` slice using the provided `FsFFTSettings`.
+///
+/// It will return an parity data number of elements of the same length because it will use the FFT to
+/// expand the input to 2n elements.
+///
+/// # Arguments
+///
+/// * `fs` - A reference to an `FsFFTSettings` instance.
+/// * `source` - A slice of `BlsScalar` to extend. The length of the slice must be a power of two.
+///
+/// # Returns
+///
+/// Returns a `Result` containing a `Vec` of extended `BlsScalar` instances or an error message.
 pub fn extend(fs: &FsFFTSettings, source: &[BlsScalar]) -> Result<Vec<BlsScalar>, String> {
 	fs.das_fft_extension(BlsScalar::slice_to_repr(source))
 		.map(BlsScalar::vec_from_repr)
 }
 
+/// Extends the given `Polynomial` instance using the provided `FsFFTSettings`.
+///
+/// It returns data that has been extended to twice its length and has been processed with `reverse_bit_order`,
+/// making it directly applicable to data sampling.
+///
+/// # Arguments
+///
+/// * `fs` - A reference to an `FsFFTSettings` instance.
+/// * `poly` - A reference to a `Polynomial` instance to extend.
+///
+/// # Returns
+///
+/// Returns a `Result` containing a `Vec` of extended `BlsScalar` instances or an error message.
 pub fn extend_poly(fs: &FsFFTSettings, poly: &Polynomial) -> Result<Vec<BlsScalar>, String> {
 	let mut coeffs = poly.0.coeffs.clone();
 	coeffs.resize(coeffs.len() * 2, FsFr::zero());
@@ -36,6 +62,20 @@ pub fn extend_poly(fs: &FsFFTSettings, poly: &Polynomial) -> Result<Vec<BlsScala
 	Ok(BlsScalar::vec_from_repr(extended_coeffs_fft))
 }
 
+/// Extends the given slice of `T` instances using the provided `FsFFTSettings` and `FsG1` scalar field.
+///
+/// This is used to extend data for `KZGCommitment` and `KZGProof`, both of which are of type `FsG1`.
+/// It returns a result that interleaves the original data with parity data, so column extensions need
+/// to be handled separately.
+///
+/// # Arguments
+///
+/// * `fs` - A reference to an `FsFFTSettings` instance.
+/// * `source` - A slice of `T` instances to extend.
+///
+/// # Returns
+///
+/// Returns a `Result` containing a `Vec` of extended `T` instances or an error message.
 pub fn extend_fs_g1<T: ReprConvert<FsG1>>(
 	fs: &FsFFTSettings,
 	source: &[T],
@@ -45,33 +85,57 @@ pub fn extend_fs_g1<T: ReprConvert<FsG1>>(
 	fs.fft_g1(&coeffs, false).map(T::vec_from_repr)
 }
 
+/// Recovers the original data from the given `shards` slice using the provided `FsFFTSettings`.
+///
+/// The `shards` slice should contain more than half of the valid data, otherwise it will not be
+/// possible to recover the original data and an error will be returned. If the `shards` slice
+/// contains `None`, the function will return the original data.
+///
+/// # Arguments
+///
+/// * `fs` - A reference to an `FsFFTSettings` instance.
+/// * `shards` - A slice of `Option<BlsScalar>` instances to recover data from.
+///
+/// # Returns
+///
+/// Returns a `Result` containing a `Vec` of recovered `BlsScalar` instances or an error message.
 pub fn recover(fs: &FsFFTSettings, shards: &[Option<BlsScalar>]) -> Result<Vec<BlsScalar>, String> {
 	match shards.contains(&None) {
 		true => {
-			let poly = FsPoly::recover_poly_from_samples(BlsScalar::slice_option_to_repr(shards), &fs)?;
+			let poly =
+				FsPoly::recover_poly_from_samples(BlsScalar::slice_option_to_repr(shards), &fs)?;
 			Ok(BlsScalar::vec_from_repr(poly.coeffs))
 		},
 		false => {
-			// shards 中不包含 None ，它是安全的
+			// shards does not contain None, it is safe to unwrap
 			Ok(shards.iter().map(|s| s.unwrap()).collect::<Vec<BlsScalar>>())
 		},
 	}
 }
 
+/// Recovers a polynomial from the given shards using the provided FFT settings.
+/// 
+/// It checks if `shards` contains no `None` values, and if so, directly computes the polynomial using FFT.
+/// This also prevents errors when `shards` contains no `None` values.
+///
+/// # Arguments
+///
+/// * `fs` - FFT settings to use for the recovery.
+/// * `shards` - Shards to recover the polynomial from.
 pub fn recover_poly(
 	fs: &FsFFTSettings,
 	shards: &[Option<BlsScalar>],
 ) -> Result<Polynomial, String> {
-	// 检查 shards 前半部分是否没有 none ，如果没有，则使用快速傅里叶直接计算
-	// 同时也是防止整个shares 没有 none 的情况下，引起错误
-	
 	let mut poly = match shards.contains(&None) {
 		true => {
-			let poly = FsPoly::recover_poly_coeffs_from_samples(BlsScalar::slice_option_to_repr(shards), &fs)?;
+			let poly = FsPoly::recover_poly_coeffs_from_samples(
+				BlsScalar::slice_option_to_repr(shards),
+				&fs,
+			)?;
 			Polynomial::from(poly)
 		},
 		false => {
-			// shards 中不包含 None ，它是安全的
+			// shards does not contain None, it is safe
 			let data = shards.iter().map(|s| s.unwrap()).collect::<Vec<BlsScalar>>();
 			let coeffs = fs.fft_fr(BlsScalar::slice_to_repr(&data), true).expect("");
 			Polynomial::from_coeffs(&coeffs)
@@ -81,4 +145,4 @@ pub fn recover_poly(
 	poly.left();
 
 	Ok(poly)
-}
\ No newline at end of file
+}