diff --git a/src/klotski_core/raw_code/mirror.cc b/src/klotski_core/raw_code/mirror.cc
index d419383..76173bd 100644
--- a/src/klotski_core/raw_code/mirror.cc
+++ b/src/klotski_core/raw_code/mirror.cc
@@ -2,37 +2,17 @@
 
 using klotski::RawCode;
 
-/// Static mirror functions
-bool RawCode::is_vertical_mirror(RawCode &&raw_code) {
-    return raw_code.is_vertical_mirror();
-}
-
-bool RawCode::is_horizontal_mirror(RawCode &&raw_code) {
-    return raw_code.is_horizontal_mirror();
-}
-
-bool RawCode::is_vertical_mirror(const RawCode &raw_code) {
-    return raw_code.is_vertical_mirror();
-}
+/// Mirror convert functions
+RawCode RawCode::to_vertical_mirror() const {
 
-bool RawCode::is_horizontal_mirror(const RawCode &raw_code) {
-    return raw_code.is_horizontal_mirror();
-}
+    // TODO: vertical mirror convert
 
-RawCode RawCode::to_vertical_mirror(RawCode &&raw_code) {
-    return raw_code.to_vertical_mirror();
 }
 
-RawCode RawCode::to_horizontal_mirror(RawCode &&raw_code) {
-    return raw_code.to_horizontal_mirror();
-}
+RawCode RawCode::to_horizontal_mirror() const {
 
-RawCode RawCode::to_vertical_mirror(const RawCode &raw_code) {
-    return raw_code.to_vertical_mirror();
-}
+    // TODO: horizontal mirror convert
 
-RawCode RawCode::to_horizontal_mirror(const RawCode &raw_code) {
-    return raw_code.to_horizontal_mirror();
 }
 
 /// Mirror check functions
@@ -48,15 +28,26 @@ bool RawCode::is_horizontal_mirror() const {
 
 }
 
-/// Mirror convert functions
-RawCode RawCode::to_vertical_mirror() const {
+bool RawCode::is_vertical_mirror(RawCode &&raw_code) const {
 
-    // TODO: vertical mirror convert
+    // TODO: vertical mirror check
 
 }
 
-RawCode RawCode::to_horizontal_mirror() const {
+bool RawCode::is_vertical_mirror(const RawCode &raw_code) const {
 
-    // TODO: horizontal mirror convert
+    // TODO: vertical mirror check
+
+}
+
+bool RawCode::is_horizontal_mirror(RawCode &&raw_code) const {
+
+    // TODO: horizontal mirror check
+
+}
+
+bool RawCode::is_horizontal_mirror(const RawCode &raw_code) const {
+
+    // TODO: horizontal mirror check
 
 }
diff --git a/src/klotski_core/raw_code/raw_code.h b/src/klotski_core/raw_code/raw_code.h
index 1f4e797..230eff1 100644
--- a/src/klotski_core/raw_code/raw_code.h
+++ b/src/klotski_core/raw_code/raw_code.h
@@ -91,20 +91,15 @@ namespace klotski {
         static RawCode from_common_code(const std::string &common_code);
 
         /// Mirror functions
-        bool is_vertical_mirror() const;
-        bool is_horizontal_mirror() const;
-
         RawCode to_vertical_mirror() const;
         RawCode to_horizontal_mirror() const;
 
-        static bool is_vertical_mirror(RawCode &&raw_code);
-        static bool is_horizontal_mirror(RawCode &&raw_code);
-        static bool is_vertical_mirror(const RawCode &raw_code);
-        static bool is_horizontal_mirror(const RawCode &raw_code);
+        bool is_vertical_mirror() const; // whether vertically symmetrical
+        bool is_horizontal_mirror() const; // whether horizontally symmetrical
 
-        static RawCode to_vertical_mirror(RawCode &&raw_code);
-        static RawCode to_horizontal_mirror(RawCode &&raw_code);
-        static RawCode to_vertical_mirror(const RawCode &raw_code);
-        static RawCode to_horizontal_mirror(const RawCode &raw_code);
+        bool is_vertical_mirror(RawCode &&raw_code) const; // whether vertically symmetric to another
+        bool is_vertical_mirror(const RawCode &raw_code) const;
+        bool is_horizontal_mirror(RawCode &&raw_code) const; // whether horizontally symmetric to another
+        bool is_horizontal_mirror(const RawCode &raw_code) const;
     };
 }
diff --git a/src/klotski_core/short_code/convert.cc b/src/klotski_core/short_code/convert.cc
index 992c74b..598e28a 100644
--- a/src/klotski_core/short_code/convert.cc
+++ b/src/klotski_core/short_code/convert.cc
@@ -10,7 +10,7 @@ using klotski::ShortCode;
 using klotski::CommonCode;
 
 /// ShortCode to CommonCode
-CommonCode ShortCode::to_common_code() const { // convert to common code
+CommonCode ShortCode::to_common_code() const {
     if (ShortCode::mode() == ShortCode::NORMAL) {
         return CommonCode::unsafe_create(tiny_decode(code)); // normal mode
     }
@@ -18,10 +18,34 @@ CommonCode ShortCode::to_common_code() const { // convert to common code
 }
 
 /// CommonCode to ShortCode
+ShortCode::ShortCode(CommonCode &&common_code) {
+    if (ShortCode::mode() == ShortCode::NORMAL) {
+        code = tiny_encode(common_code.unwrap()); // normal mode
+    } else {
+        code = fast_encode(common_code.unwrap()); // fast mode
+    }
+}
+
+ShortCode::ShortCode(const CommonCode &common_code) {
+    if (ShortCode::mode() == ShortCode::NORMAL) {
+        code = tiny_encode(common_code.unwrap()); // normal mode
+    } else {
+        code = fast_encode(common_code.unwrap()); // fast mode
+    }
+}
+
 ShortCode ShortCode::from_common_code(uint64_t common_code) {
     return ShortCode(CommonCode(common_code));
 }
 
+ShortCode ShortCode::from_common_code(CommonCode &&common_code) {
+    return ShortCode(std::forward<CommonCode>(common_code));
+}
+
+ShortCode ShortCode::from_common_code(std::string &&common_code) {
+    return ShortCode(std::forward<std::string>(common_code));
+}
+
 ShortCode ShortCode::from_common_code(const CommonCode &common_code) {
     return ShortCode(common_code);
 }
@@ -30,14 +54,6 @@ ShortCode ShortCode::from_common_code(const std::string &common_code) {
     return ShortCode(CommonCode(common_code));
 }
 
-ShortCode::ShortCode(const CommonCode &common_code) { // convert from common code
-    if (ShortCode::mode() == ShortCode::NORMAL) {
-        code = tiny_encode(common_code.unwrap()); // normal mode
-    } else {
-        code = fast_encode(common_code.unwrap()); // fast mode
-    }
-}
-
 /// 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 26e107d..428ff99 100644
--- a/src/klotski_core/short_code/serialize.cc
+++ b/src/klotski_core/short_code/serialize.cc
@@ -4,10 +4,7 @@
 using klotski::ShortCode;
 using klotski::ShortCodeException;
 
-ShortCode ShortCode::from_string(const std::string &short_code) {
-    return ShortCode(short_code); // convert from 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
@@ -19,7 +16,24 @@ std::string ShortCode::to_string() const { // encode as 5-bits string
     return result;
 }
 
-ShortCode::ShortCode(const std::string &short_code) { // 5-bits string decode
+/// String to ShortCode
+ShortCode::ShortCode(std::string &&short_code) {
+    code = string_decode(short_code);
+}
+
+ShortCode::ShortCode(const std::string &short_code) {
+    code = string_decode(short_code);
+}
+
+ShortCode ShortCode::from_string(std::string &&short_code) {
+    return ShortCode(short_code);
+}
+
+ShortCode ShortCode::from_string(const std::string &short_code) {
+    return ShortCode(short_code);
+}
+
+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");
     }
@@ -40,5 +54,5 @@ ShortCode::ShortCode(const std::string &short_code) { // 5-bits string decode
     if (!ShortCode::check(result)) { // check converted short code
         throw ShortCodeException("short code invalid");
     }
-    code = result; // apply convert result
+    return result; // apply convert result
 }
diff --git a/src/klotski_core/short_code/short_code.cc b/src/klotski_core/short_code/short_code.cc
index 029cfbb..fcb67d0 100644
--- a/src/klotski_core/short_code/short_code.cc
+++ b/src/klotski_core/short_code/short_code.cc
@@ -18,6 +18,10 @@ namespace std {
 }
 
 namespace klotski {
+    bool ShortCode::operator==(uint32_t short_code) const {
+        return this->code == short_code;
+    }
+
     bool ShortCode::operator==(const ShortCode &short_code) const {
         return this->code == short_code.code;
     }
@@ -51,15 +55,15 @@ namespace klotski {
     }
 }
 
-bool klotski::ShortCode::check(uint32_t short_code) {
-    return short_code < SHORT_CODE_LIMIT; // 0 ~ (SHORT_CODE_LIMIT - 1)
-}
-
 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)
+}
+
 ShortCode::Mode ShortCode::mode() { // ensure speed up enabled and return current mode
     if (fast_mode_available) {
         return ShortCode::FAST; // fast mode already enabled
diff --git a/src/klotski_core/short_code/short_code.h b/src/klotski_core/short_code/short_code.h
index de84df0..9ba17ea 100644
--- a/src/klotski_core/short_code/short_code.h
+++ b/src/klotski_core/short_code/short_code.h
@@ -53,11 +53,14 @@
 #include <ostream>
 #include <stdexcept>
 #include <utility>
+#include "all_cases.h"
 #include "common_code.h"
 
 namespace klotski {
     class CommonCode; // import for convert interface
 
+    const uint32_t SHORT_CODE_LIMIT = klotski::ALL_CASES_SIZE_SUM;
+
     class ShortCodeException : public std::runtime_error {
     public:
         ShortCodeException() : std::runtime_error("invalid short code") {}
@@ -73,15 +76,16 @@ namespace klotski {
         uint32_t code;
         ShortCode() = default; // unsafe initialize
 
-        static Mode mode();
+        static inline Mode mode();
         static bool fast_mode_available;
         static bool normal_mode_available;
+
         static uint64_t fast_decode(uint32_t short_code); // short code -> common code
         static uint32_t fast_encode(uint64_t common_code); // common code -> short code
         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 const uint32_t SHORT_CODE_LIMIT = 29334498;
+        static uint32_t string_decode(const std::string &short_code); // string -> short code
 
     public:
         /// ShortCode validity check
@@ -109,12 +113,6 @@ namespace klotski {
         explicit ShortCode(const std::string &short_code);
         explicit ShortCode(const CommonCode &common_code);
 
-        ShortCode(uint32_t short_code, Mode mode) : ShortCode(short_code) { speed_up(mode); }
-        ShortCode(const std::string &short_code, Mode mode) : ShortCode(short_code) { speed_up(mode); }
-        ShortCode(const CommonCode &common_code, Mode mode) : ShortCode(common_code) { speed_up(mode); }
-        ShortCode(std::string &&short_code, Mode mode) : ShortCode(std::forward<std::string>(short_code)) { speed_up(mode); }
-        ShortCode(CommonCode &&common_code, Mode mode) : ShortCode(std::forward<CommonCode>(common_code)) { speed_up(mode); }
-
         /// Static initialization
         static ShortCode create(uint32_t short_code);
         static ShortCode unsafe_create(uint32_t short_code);