diff --git a/cauchy_reed_solomon_erasure_coding.hh b/cauchy_reed_solomon_erasure_coding.hh
new file mode 100644
index 0000000..703d5c3
--- /dev/null
+++ b/cauchy_reed_solomon_erasure_coding.hh
@@ -0,0 +1,104 @@
+/*
+Cauchy Reed Solomon Erasure Coding
+
+Copyright 2023 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+namespace CODE {
+
+template <typename GF>
+struct CauchyReedSolomonEncoder
+{
+	typedef typename GF::value_type value_type;
+	typedef typename GF::ValueType ValueType;
+	typedef typename GF::IndexType IndexType;
+	// $a_{ij} = \frac{1}{x_i + y_j}$
+	IndexType cauchy_matrix(int i, int j)
+	{
+		ValueType row(i), col(ValueType::N - j);
+		return rcp(index(row + col));
+	}
+	void operator()(const ValueType *data, ValueType *block, int block_num, int block_len, int block_cnt)
+	{
+		assert(block_num <= ValueType::N - block_cnt);
+		for (int k = 0; k < block_cnt; k++) {
+			IndexType a_ik = cauchy_matrix(block_num, k);
+			for (int j = 0; j < block_len; j++) {
+				if (k)
+					block[j] = fma(a_ik, data[block_len*k+j], block[j]);
+				else
+					block[j] = a_ik * data[block_len*k+j];
+			}
+		}
+	}
+	void operator()(const value_type *data, value_type *block, int block_num, int block_len, int block_cnt)
+	{
+		(*this)(reinterpret_cast<const ValueType *>(data), reinterpret_cast<ValueType *>(block), block_num, block_len, block_cnt);
+	}
+	void operator()(const void *data, void *block, int block_number, int block_bytes, int block_count)
+	{
+		assert(block_bytes % sizeof(value_type) == 0);
+		(*this)(reinterpret_cast<const value_type *>(data), reinterpret_cast<value_type *>(block), block_number, block_bytes / sizeof(value_type), block_count);
+	}
+};
+
+template <typename GF>
+struct CauchyReedSolomonDecoder
+{
+	typedef typename GF::value_type value_type;
+	typedef typename GF::ValueType ValueType;
+	typedef typename GF::IndexType IndexType;
+	// $b_{ij} = \frac{\prod_{k=1}^{n}{(x_j + y_k)(x_k + y_i)}}{(x_j + y_i)\prod_{k \ne j}^{n}{(x_j - x_k)}\prod_{k \ne i}^{n}{(y_i - y_k)}}$
+	IndexType inverse_cauchy_matrix(const ValueType *rows, int i, int j, int n)
+	{
+		ValueType col_i(ValueType::N - i);
+		IndexType prod_xy(0);
+		for (int k = 0; k < n; k++) {
+			ValueType col_k(ValueType::N - k);
+			prod_xy *= index(rows[j] + col_k) * index(rows[k] + col_i);
+		}
+		IndexType prod_x(0);
+		for (int k = 0; k < n; k++) {
+			if (k != j) {
+				prod_x *= index(rows[j] + rows[k]);
+			}
+		}
+		IndexType prod_y(0);
+		for (int k = 0; k < n; k++) {
+			if (k != i) {
+				ValueType col_k(ValueType::N - k);
+				prod_y *= index(col_i + col_k);
+			}
+		}
+		return prod_xy / (index(rows[j] + col_i) * prod_x * prod_y);
+	}
+	void operator()(ValueType *data, const ValueType *blocks, const ValueType *block_nums, int block_len, int block_cnt)
+	{
+		for (int i = 0; i < block_cnt; i++) {
+			for (int k = 0; k < block_cnt; k++) {
+				IndexType b_ik = inverse_cauchy_matrix(block_nums, i, k, block_cnt);
+				for (int j = 0; j < block_len; j++) {
+					if (k)
+						data[j] = fma(b_ik, blocks[block_len*k+j], data[j]);
+					else
+						data[j] = b_ik * blocks[block_len*k+j];
+				}
+			}
+			data += block_len;
+		}
+	}
+	void operator()(value_type *data, const value_type *blocks, const value_type *block_nums, int block_len, int block_cnt)
+	{
+		(*this)(reinterpret_cast<ValueType *>(data), reinterpret_cast<const ValueType *>(blocks), reinterpret_cast<const ValueType *>(block_nums), block_len, block_cnt);
+	}
+	void operator()(void *data, const void *blocks, const value_type *block_numbers, int block_bytes, int block_count)
+	{
+		assert(block_bytes % sizeof(value_type) == 0);
+		(*this)(reinterpret_cast<value_type *>(data), reinterpret_cast<const value_type *>(blocks), block_numbers, block_bytes / sizeof(value_type), block_count);
+	}
+};
+
+}
+
diff --git a/tests/crs_regression_test.cc b/tests/crs_regression_test.cc
new file mode 100644
index 0000000..210abcf
--- /dev/null
+++ b/tests/crs_regression_test.cc
@@ -0,0 +1,70 @@
+/*
+Regression Test for the Cauchy Reed Solomon Encoder and Decoder
+
+Copyright 2023 Ahmet Inan <inan@aicodix.de>
+*/
+
+#include <cassert>
+#include <random>
+#include <iostream>
+#include <functional>
+#include "galois_field.hh"
+#include "cauchy_reed_solomon_erasure_coding.hh"
+
+template <typename GF>
+void crs_test(int trials)
+{
+	CODE::CauchyReedSolomonEncoder<GF> encode;
+	CODE::CauchyReedSolomonDecoder<GF> decode;
+	std::random_device rd;
+	std::default_random_engine generator(rd());
+	typedef std::uniform_int_distribution<int> distribution;
+	auto rnd_cnt = std::bind(distribution(1, std::min(GF::Q / 2, 256)), generator);
+	auto rnd_len = std::bind(distribution(1, 1 << 10), generator);
+	auto rnd_dat = std::bind(distribution(0, 255), generator);
+	while (--trials) {
+		int block_count = rnd_cnt();
+		int numbers_total = GF::Q - block_count;
+		int block_bytes = rnd_len() * sizeof(typename GF::value_type);
+		int data_bytes = block_count * block_bytes;
+		uint8_t *orig = new uint8_t[data_bytes];
+		for (int i = 0; i < data_bytes; ++i)
+			orig[i] = rnd_dat();
+		uint8_t *blocks = new uint8_t[data_bytes];
+		auto numbers = new typename GF::value_type[numbers_total];
+		for (int i = 0; i < numbers_total; ++i)
+			numbers[i] = i;
+		for (int i = 0; i < block_count; i++) {
+			auto hat = std::bind(distribution(i, numbers_total - 1), generator);
+			std::swap(numbers[i], numbers[hat()]);
+		}
+		for (int i = 0; i < block_count; ++i)
+			encode(orig, blocks + block_bytes * i, numbers[i], block_bytes, block_count);
+		uint8_t *data = new uint8_t[data_bytes];
+		decode(data, blocks, numbers, block_bytes, block_count);
+		for (int i = 0; i < data_bytes; ++i)
+			assert(data[i] == orig[i]);
+		delete[] numbers;
+		delete[] blocks;
+		delete[] orig;
+		delete[] data;
+	}
+}
+
+int main()
+{
+	if (1) {
+		typedef CODE::GaloisField<8, 0b100011101, uint8_t> GF;
+		GF instance;
+		crs_test<GF>(200);
+	}
+	if (1) {
+		typedef CODE::GaloisField<16, 0b10001000000001011, uint16_t> GF;
+		GF *instance = new GF();
+		crs_test<GF>(100);
+		delete instance;
+	}
+	std::cerr << "Cauchy Reed Solomon regression test passed!" << std::endl;
+	return 0;
+}
+