diff --git a/src/klotski_core/common_code/common_code.cc b/src/klotski_core/common_code/common_code.cc
index 5230c4f..198a8d6 100644
--- a/src/klotski_core/common_code/common_code.cc
+++ b/src/klotski_core/common_code/common_code.cc
@@ -1,6 +1,8 @@
 #include "common.h"
 #include "common_code.h"
 
+using klotski::CommonCode;
+
 namespace std {
     template<>
     struct hash<klotski::CommonCode> {
@@ -18,6 +20,10 @@ namespace std {
 }
 
 namespace klotski {
+    bool CommonCode::operator==(uint64_t common_code) const {
+        return this->code == common_code;
+    }
+
     bool CommonCode::operator==(const CommonCode &common_code) const {
         return this->code == common_code.code;
     }
@@ -53,7 +59,7 @@ namespace klotski {
     }
 }
 
-bool klotski::CommonCode::check(uint64_t common_code) { // whether common code is valid
+bool CommonCode::check(uint64_t common_code) { // whether common code is valid
     ///   M_1x1     M_1x2     M_2x1     M_2x2
     ///  1 0 0 0   1 1 0 0   1 0 0 0   1 1 0 0
     ///  0 0 0 0   0 0 0 0   1 0 0 0   1 1 0 0
diff --git a/src/klotski_core/common_code/common_code.h b/src/klotski_core/common_code/common_code.h
index 6bf2f3c..e82dca3 100644
--- a/src/klotski_core/common_code/common_code.h
+++ b/src/klotski_core/common_code/common_code.h
@@ -59,8 +59,7 @@
 #include "short_code.h"
 
 namespace klotski {
-    // import for convert interface
-    class RawCode;
+    class RawCode; // import for convert interface
     class ShortCode;
 
     class CommonCodeException : public std::runtime_error {
@@ -71,11 +70,19 @@ namespace klotski {
     };
 
     class CommonCode {
+        uint64_t code;
+        CommonCode() = default; // unsafe initialize
+
+        static inline uint64_t string_decode(const std::string &common_code);
+        static inline std::string string_encode(uint64_t common_code, bool shorten);
+
     public:
+        /// CommonCode validity check
         bool valid() const;
         static bool check(uint64_t common_code);
 
         /// Operators of CommonCode
+        bool operator==(uint64_t common_code) const;
         bool operator==(const CommonCode &common_code) const;
         constexpr explicit operator uint64_t() const { return code; }
         friend std::ostream& operator<<(std::ostream &out, const CommonCode &self);
@@ -88,24 +95,28 @@ namespace klotski {
 
         /// CommonCode constructors
         explicit CommonCode(uint64_t common_code);
+        explicit CommonCode(RawCode &&raw_code);
+        explicit CommonCode(ShortCode &&short_code);
+        explicit CommonCode(std::string &&common_code);
         explicit CommonCode(const RawCode &raw_code);
         explicit CommonCode(const ShortCode &short_code);
         explicit CommonCode(const std::string &common_code);
 
-        /// Rust-style initialization
+        /// Static initialization
         static CommonCode create(uint64_t common_code);
         static CommonCode unsafe_create(uint64_t common_code);
+
+        static CommonCode from_string(std::string &&common_code);
         static CommonCode from_string(const std::string &common_code);
 
         static CommonCode from_raw_code(uint64_t raw_code);
+        static CommonCode from_raw_code(RawCode &&raw_code);
         static CommonCode from_raw_code(const RawCode &raw_code);
 
         static CommonCode from_short_code(uint32_t short_code);
+        static CommonCode from_short_code(ShortCode &&short_code);
+        static CommonCode from_short_code(std::string &&short_code);
         static CommonCode from_short_code(const ShortCode &short_code);
         static CommonCode from_short_code(const std::string &short_code);
-
-    private:
-        uint64_t code;
-        CommonCode() = default; // unsafe initialize
     };
 }
diff --git a/src/klotski_core/common_code/convert.cc b/src/klotski_core/common_code/convert.cc
index 7675688..28d023c 100644
--- a/src/klotski_core/common_code/convert.cc
+++ b/src/klotski_core/common_code/convert.cc
@@ -4,34 +4,62 @@ using klotski::RawCode;
 using klotski::ShortCode;
 using klotski::CommonCode;
 
-/// CommonCode to RawCode
+/// -------------------------- CommonCode to RawCode --------------------------
+
 RawCode CommonCode::to_raw_code() const {
     return RawCode(*this); // convert to raw code
 }
 
-/// CommonCode to ShortCode
+/// ------------------------- CommonCode to ShortCode -------------------------
+
 ShortCode CommonCode::to_short_code() const {
     return ShortCode(*this); // convert to short code
 }
 
-/// RawCode to CommonCode
+/// -------------------------- RawCode to CommonCode --------------------------
+
 CommonCode CommonCode::from_raw_code(uint64_t raw_code) {
     return RawCode(raw_code).to_common_code();
 }
 
+CommonCode CommonCode::from_raw_code(RawCode &&raw_code) {
+    return raw_code.to_common_code();
+}
+
 CommonCode CommonCode::from_raw_code(const RawCode &raw_code) {
     return raw_code.to_common_code();
 }
 
+CommonCode::CommonCode(RawCode &&raw_code) {
+    code = raw_code.to_common_code().code; // convert from raw code
+}
+
 CommonCode::CommonCode(const RawCode &raw_code) {
     code = raw_code.to_common_code().code; // convert from raw code
 }
 
-/// ShortCode to CommonCode
+/// ------------------------- ShortCode to CommonCode -------------------------
+
+CommonCode::CommonCode(ShortCode &&short_code) {
+    code = short_code.to_common_code().code; // convert from short code
+}
+
+CommonCode::CommonCode(const ShortCode &short_code) {
+    code = short_code.to_common_code().code; // convert from short code
+}
+
 CommonCode CommonCode::from_short_code(uint32_t short_code) {
     return ShortCode(short_code).to_common_code();
 }
 
+CommonCode CommonCode::from_short_code(ShortCode &&short_code) {
+    return short_code.to_common_code();
+}
+
+CommonCode CommonCode::from_short_code(std::string &&short_code) {
+    return ShortCode(std::forward<std::string>(short_code)).to_common_code();
+}
+
 CommonCode CommonCode::from_short_code(const ShortCode &short_code) {
     return short_code.to_common_code();
 }
@@ -39,7 +67,3 @@ CommonCode CommonCode::from_short_code(const ShortCode &short_code) {
 CommonCode CommonCode::from_short_code(const std::string &short_code) {
     return ShortCode(short_code).to_common_code();
 }
-
-CommonCode::CommonCode(const ShortCode &short_code) {
-    code = short_code.to_common_code().code; // convert from short code
-}
diff --git a/src/klotski_core/common_code/serialize.cc b/src/klotski_core/common_code/serialize.cc
index 81bf169..7bee4b9 100644
--- a/src/klotski_core/common_code/serialize.cc
+++ b/src/klotski_core/common_code/serialize.cc
@@ -3,6 +3,32 @@
 using klotski::CommonCode;
 using klotski::CommonCodeException;
 
+/// -------------------------- CommonCode to String ---------------------------
+
+std::string CommonCode::to_string(bool shorten) const {
+    return string_encode(code, shorten);
+}
+
+/// -------------------------- String to CommonCode ---------------------------
+
+CommonCode::CommonCode(std::string &&common_code) {
+    code = string_decode(common_code); // load from string
+}
+
+CommonCode::CommonCode(const std::string &common_code) {
+    code = string_decode(common_code); // load from string
+}
+
+CommonCode CommonCode::from_string(std::string &&common_code) {
+    return CommonCode(std::forward<std::string>(common_code));
+}
+
+CommonCode CommonCode::from_string(const std::string &common_code) {
+    return CommonCode(common_code);
+}
+
+/// ----------------------------- Basic Functions -----------------------------
+
 inline uint8_t binary_count(uint32_t bin) { // get number of non-zero bits
     bin -= (bin >> 1) & 0x55'55'55'55;
     bin = (bin & 0x33'33'33'33) + ((bin >> 2) & 0x33'33'33'33);
@@ -18,28 +44,25 @@ inline uint8_t last_zero_num(uint32_t bin) { // get last zero number
     return binary_count(bin >> 1);
 }
 
-CommonCode CommonCode::from_string(const std::string &common_code) {
-    return CommonCode(common_code); // load from string
-}
-
-std::string CommonCode::to_string(bool shorten) const { // convert uint64_t code to string
+std::string CommonCode::string_encode(uint64_t common_code, bool shorten) { // convert uint64_t code to string
     char result[10]; // max length 9-bits
-    sprintf(result, "%09lX", code);
+    sprintf(result, "%09lX", common_code);
     if (shorten) { // remove `0` after common code
-        if ((uint32_t)code == 0x00'00'00'00) { // low 32-bits are zero
+        if ((uint32_t)common_code == 0x00'00'00'00) { // low 32-bits are zero
             result[1] = '\0'; // only keep first character
             return result;
         }
-        result[9 - last_zero_num(code) / 4] = '\0'; // truncate string
+        result[9 - last_zero_num(common_code) / 4] = '\0'; // truncate string
     }
     return result; // char* -> std::string
 }
 
-CommonCode::CommonCode(const std::string &common_code) { // convert from 1 ~ 9 bits string
+uint64_t CommonCode::string_decode(const std::string &common_code) { // convert from 1 ~ 9 bits string
     /// check string length
     if (common_code.length() > 9 || common_code.empty()) { // check string length
         throw CommonCodeException("common code should length 1 ~ 9");
     }
+
     /// check every characters
     uint64_t result = 0;
     for (auto const &bit : common_code) {
@@ -55,9 +78,10 @@ CommonCode::CommonCode(const std::string &common_code) { // convert from 1 ~ 9 b
         }
     }
     result <<= (9 - common_code.length()) * 4; // low-bits fill with zero
+
     /// check whether common code is valid
     if (!CommonCode::check(result)) { // check converted common code
         throw CommonCodeException("common code invalid");
     }
-    code = result;
+    return result;
 }
diff --git a/src/klotski_core/raw_code/convert.cc b/src/klotski_core/raw_code/convert.cc
index a0434e2..cd5c841 100644
--- a/src/klotski_core/raw_code/convert.cc
+++ b/src/klotski_core/raw_code/convert.cc
@@ -5,18 +5,20 @@ using klotski::RawCode;
 using klotski::CommonCode;
 using klotski::RawCodeException;
 
-/// RawCode to CommonCode
+/// -------------------------- RawCode to CommonCode --------------------------
+
 CommonCode RawCode::to_common_code() const {
     return CommonCode::unsafe_create(RawCode::compact(code));
 }
 
-/// CommonCode to RawCode
+/// -------------------------- CommonCode to RawCode --------------------------
+
 RawCode::RawCode(CommonCode &&common_code) {
-    code = RawCode::extract(common_code.unwrap());
+    code = RawCode::extract(common_code.unwrap()); // convert from common code
 }
 
 RawCode::RawCode(const CommonCode &common_code) {
-    code = RawCode::extract(common_code.unwrap());
+    code = RawCode::extract(common_code.unwrap()); // convert from common code
 }
 
 RawCode RawCode::from_common_code(uint64_t common_code) {
@@ -39,6 +41,8 @@ RawCode RawCode::from_common_code(const std::string &common_code) {
     return RawCode(CommonCode(common_code));
 }
 
+/// ----------------------------- Basic Functions -----------------------------
+
 /// NOTE: ensure that input raw code is valid!
 uint64_t RawCode::compact(uint64_t raw_code) { // raw code --> common code
     int unfilled = 16;
diff --git a/src/klotski_core/raw_code/mirror.cc b/src/klotski_core/raw_code/mirror.cc
index 76173bd..46b5d1f 100644
--- a/src/klotski_core/raw_code/mirror.cc
+++ b/src/klotski_core/raw_code/mirror.cc
@@ -4,15 +4,11 @@ using klotski::RawCode;
 
 /// Mirror convert functions
 RawCode RawCode::to_vertical_mirror() const {
-
-    // TODO: vertical mirror convert
-
+    return RawCode::unsafe_create(vertical_mirror(code));
 }
 
 RawCode RawCode::to_horizontal_mirror() const {
-
-    // TODO: horizontal mirror convert
-
+    return RawCode::unsafe_create(horizontal_mirror(code));
 }
 
 /// Mirror check functions
@@ -20,34 +16,55 @@ bool RawCode::is_vertical_mirror() const {
 
     // TODO: vertical mirror check
 
+    return false;
 }
 
 bool RawCode::is_horizontal_mirror() const {
 
     // TODO: horizontal mirror check
 
+    return false;
 }
 
 bool RawCode::is_vertical_mirror(RawCode &&raw_code) const {
 
     // TODO: vertical mirror check
 
+    return false;
 }
 
 bool RawCode::is_vertical_mirror(const RawCode &raw_code) const {
 
     // TODO: vertical mirror check
 
+    return false;
 }
 
 bool RawCode::is_horizontal_mirror(RawCode &&raw_code) const {
 
     // TODO: horizontal mirror check
 
+    return false;
 }
 
 bool RawCode::is_horizontal_mirror(const RawCode &raw_code) const {
 
     // TODO: horizontal mirror check
 
+    return false;
+}
+
+/// Basic mirror convert
+uint64_t RawCode::vertical_mirror(uint64_t raw_code) {
+
+    // TODO: vertical mirror convert
+
+    return 0;
+}
+
+uint64_t RawCode::horizontal_mirror(uint64_t raw_code) {
+
+    // TODO: horizontal mirror convert
+
+    return 0;
 }
diff --git a/src/klotski_core/raw_code/raw_code.h b/src/klotski_core/raw_code/raw_code.h
index 230eff1..b17c65d 100644
--- a/src/klotski_core/raw_code/raw_code.h
+++ b/src/klotski_core/raw_code/raw_code.h
@@ -60,6 +60,9 @@ namespace klotski {
         static uint64_t compact(uint64_t raw_code); // raw code -> common code
         static uint64_t extract(uint64_t common_code); // common code -> raw code
 
+        static uint64_t vertical_mirror(uint64_t raw_code); // to vertical mirror
+        static uint64_t horizontal_mirror(uint64_t raw_code); // to horizontal mirror
+
     public:
         /// RawCode validity check
         bool valid() const;
diff --git a/src/klotski_core/short_code/convert.cc b/src/klotski_core/short_code/convert.cc
index 598e28a..2a4e234 100644
--- a/src/klotski_core/short_code/convert.cc
+++ b/src/klotski_core/short_code/convert.cc
@@ -9,7 +9,8 @@
 using klotski::ShortCode;
 using klotski::CommonCode;
 
-/// ShortCode to CommonCode
+/// ------------------------- ShortCode to CommonCode -------------------------
+
 CommonCode ShortCode::to_common_code() const {
     if (ShortCode::mode() == ShortCode::NORMAL) {
         return CommonCode::unsafe_create(tiny_decode(code)); // normal mode
@@ -17,7 +18,8 @@ CommonCode ShortCode::to_common_code() const {
     return CommonCode::unsafe_create(fast_decode(code)); // fast mode
 }
 
-/// CommonCode to ShortCode
+/// ------------------------- ShortCode to CommonCode -------------------------
+
 ShortCode::ShortCode(CommonCode &&common_code) {
     if (ShortCode::mode() == ShortCode::NORMAL) {
         code = tiny_encode(common_code.unwrap()); // normal mode
@@ -54,6 +56,8 @@ ShortCode ShortCode::from_common_code(const std::string &common_code) {
     return ShortCode(CommonCode(common_code));
 }
 
+/// ----------------------------- Basic Functions -----------------------------
+
 /// NOTE: ensure that input common code is valid!
 uint32_t ShortCode::fast_encode(uint64_t common_code) { // common code --> short code
     auto head = common_code >> 32; // head index
diff --git a/src/klotski_core/short_code/serialize.cc b/src/klotski_core/short_code/serialize.cc
index 428ff99..23519c1 100644
--- a/src/klotski_core/short_code/serialize.cc
+++ b/src/klotski_core/short_code/serialize.cc
@@ -4,19 +4,14 @@
 using klotski::ShortCode;
 using klotski::ShortCodeException;
 
-/// ShortCode to String
+/// --------------------------- ShortCode to String ---------------------------
+
 std::string ShortCode::to_string() const { // encode as 5-bits string
-    uint32_t short_code = code;
-    char result[6]; // short code length 5
-    result[5] = '\0'; // string ending flag
-    for (int n = 0; n < 5; ++n) {
-        result[4 - n] = SHORT_CODE_TABLE[short_code & 0b11111]; // aka _ % 32
-        short_code >>= 5; // aka _ / 32
-    }
-    return result;
+    return string_encode(code);
 }
 
-/// String to ShortCode
+/// --------------------------- String to ShortCode ---------------------------
+
 ShortCode::ShortCode(std::string &&short_code) {
     code = string_decode(short_code);
 }
@@ -33,6 +28,18 @@ ShortCode ShortCode::from_string(const std::string &short_code) {
     return ShortCode(short_code);
 }
 
+/// ----------------------------- Basic Functions -----------------------------
+
+std::string klotski::ShortCode::string_encode(uint32_t short_code) { // encode as 5-bits string
+    char result[6]; // short code length 5
+    result[5] = '\0'; // string ending flag
+    for (int n = 0; n < 5; ++n) {
+        result[4 - n] = SHORT_CODE_TABLE[short_code & 0b11111]; // aka _ % 32
+        short_code >>= 5; // aka _ / 32
+    }
+    return result;
+}
+
 uint32_t ShortCode::string_decode(const std::string &short_code) { // 5-bits string decode
     if (short_code.length() != 5) { // check string length
         throw ShortCodeException("short code should length 5");
diff --git a/src/klotski_core/short_code/short_code.cc b/src/klotski_core/short_code/short_code.cc
index fcb67d0..711253d 100644
--- a/src/klotski_core/short_code/short_code.cc
+++ b/src/klotski_core/short_code/short_code.cc
@@ -1,6 +1,11 @@
 #include "all_cases.h"
 #include "short_code.h"
 
+using klotski::ShortCode;
+
+bool ShortCode::fast_mode_available = false;
+bool ShortCode::normal_mode_available = false;
+
 namespace std {
     template<>
     struct hash<klotski::ShortCode> {
@@ -55,11 +60,6 @@ namespace klotski {
     }
 }
 
-using klotski::ShortCode;
-
-bool ShortCode::fast_mode_available = false;
-bool ShortCode::normal_mode_available = false;
-
 bool ShortCode::check(uint32_t short_code) {
     return short_code < klotski::SHORT_CODE_LIMIT; // 0 ~ (SHORT_CODE_LIMIT - 1)
 }
diff --git a/src/klotski_core/short_code/short_code.h b/src/klotski_core/short_code/short_code.h
index 9ba17ea..67c959c 100644
--- a/src/klotski_core/short_code/short_code.h
+++ b/src/klotski_core/short_code/short_code.h
@@ -85,7 +85,8 @@ namespace klotski {
         static uint64_t tiny_decode(uint32_t short_code); // short code -> common code
         static uint32_t tiny_encode(uint64_t common_code); // common code -> short code
 
-        static uint32_t string_decode(const std::string &short_code); // string -> short code
+        static inline std::string string_encode(uint32_t short_code); // short code -> string
+        static inline uint32_t string_decode(const std::string &short_code); // string -> short code
 
     public:
         /// ShortCode validity check