diff --git a/src/klotski_core/common_code/common_code.cc b/src/klotski_core/common_code/common_code.cc
index 198a8d6..7530e35 100644
--- a/src/klotski_core/common_code/common_code.cc
+++ b/src/klotski_core/common_code/common_code.cc
@@ -20,14 +20,14 @@ 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;
     }
 
+    bool CommonCode::operator!=(const CommonCode &common_code) const {
+        return this->code != common_code.code;
+    }
+
     std::ostream& operator<<(std::ostream &out, const CommonCode &self) {
         char str[10];
         sprintf(str, "%09lX", self.code);
diff --git a/src/klotski_core/common_code/common_code.h b/src/klotski_core/common_code/common_code.h
index e82dca3..13f4597 100644
--- a/src/klotski_core/common_code/common_code.h
+++ b/src/klotski_core/common_code/common_code.h
@@ -82,8 +82,8 @@ namespace klotski {
         static bool check(uint64_t common_code);
 
         /// Operators of CommonCode
-        bool operator==(uint64_t common_code) const;
         bool operator==(const CommonCode &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);
 
@@ -119,4 +119,9 @@ namespace klotski {
         static CommonCode from_short_code(const ShortCode &short_code);
         static CommonCode from_short_code(const std::string &short_code);
     };
+
+    inline bool operator==(uint64_t c1, const CommonCode &c2) { return c1 == c2.unwrap(); }
+    inline bool operator!=(uint64_t c1, const CommonCode &c2) { return c1 != c2.unwrap(); }
+    inline bool operator==(const CommonCode &c1, uint64_t c2) { return c1.unwrap() == c2; }
+    inline bool operator!=(const CommonCode &c1, uint64_t c2) { return c1.unwrap() != c2; }
 }
diff --git a/src/klotski_core/raw_code/raw_code.cc b/src/klotski_core/raw_code/raw_code.cc
index a486aed..a9e24e7 100644
--- a/src/klotski_core/raw_code/raw_code.cc
+++ b/src/klotski_core/raw_code/raw_code.cc
@@ -20,10 +20,6 @@ namespace std {
 }
 
 namespace klotski {
-    bool RawCode::operator==(uint64_t raw_code) const {
-        return this->code == raw_code;
-    }
-
     bool RawCode::operator==(const RawCode &raw_code) const {
         return this->code == raw_code.code;
     }
diff --git a/src/klotski_core/raw_code/raw_code.h b/src/klotski_core/raw_code/raw_code.h
index 40852c4..0de9378 100644
--- a/src/klotski_core/raw_code/raw_code.h
+++ b/src/klotski_core/raw_code/raw_code.h
@@ -72,7 +72,6 @@ namespace klotski {
         static bool check(uint64_t raw_code);
 
         /// Operators of RawCode
-        bool operator==(uint64_t raw_code) const;
         bool operator==(const RawCode &raw_code) const;
         bool operator!=(const RawCode &raw_code) const;
         constexpr explicit operator uint64_t() const { return code; }
@@ -109,4 +108,9 @@ namespace klotski {
         bool is_horizontal_mirror(RawCode &&raw_code) const; // whether horizontally symmetric to another
         bool is_horizontal_mirror(const RawCode &raw_code) const;
     };
+
+    inline bool operator==(uint64_t r1, const RawCode &r2) { return r1 == r2.unwrap(); }
+    inline bool operator!=(uint64_t r1, const RawCode &r2) { return r1 != r2.unwrap(); }
+    inline bool operator==(const RawCode &r1, uint64_t r2) { return r1.unwrap() == r2; }
+    inline bool operator!=(const RawCode &r1, uint64_t r2) { return r1.unwrap() != r2; }
 }
diff --git a/src/klotski_core/short_code/short_code.cc b/src/klotski_core/short_code/short_code.cc
index 711253d..cde2eb1 100644
--- a/src/klotski_core/short_code/short_code.cc
+++ b/src/klotski_core/short_code/short_code.cc
@@ -23,15 +23,15 @@ 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;
     }
 
-    std::ostream &operator<<(std::ostream &out, const ShortCode &self) {
+    bool ShortCode::operator!=(const ShortCode &short_code) const {
+        return this->code != short_code.code;
+    }
+
+    std::ostream& operator<<(std::ostream &out, const ShortCode &self) {
         out << self.to_string() << "(" << self.code << ")"; // short code info
         return out;
     }
diff --git a/src/klotski_core/short_code/short_code.h b/src/klotski_core/short_code/short_code.h
index 6769047..28f0dc9 100644
--- a/src/klotski_core/short_code/short_code.h
+++ b/src/klotski_core/short_code/short_code.h
@@ -97,8 +97,8 @@ namespace klotski {
         static void speed_up(Mode mode);
 
         /// Operators of ShortCode
-        bool operator==(uint32_t short_code) const;
         bool operator==(const ShortCode &short_code) const;
+        bool operator!=(const ShortCode &short_code) const;
         constexpr explicit operator uint32_t() const { return code; }
         friend std::ostream& operator<<(std::ostream &out, const ShortCode &self);
 
@@ -127,4 +127,9 @@ namespace klotski {
         static ShortCode from_common_code(const CommonCode &common_code);
         static ShortCode from_common_code(const std::string &common_code);
     };
+
+    inline bool operator==(uint32_t s1, const ShortCode &s2) { return s1 == s2.unwrap(); }
+    inline bool operator!=(uint32_t s1, const ShortCode &s2) { return s1 != s2.unwrap(); }
+    inline bool operator==(const ShortCode &s1, uint32_t s2) { return s1.unwrap() == s2; }
+    inline bool operator!=(const ShortCode &s1, uint32_t s2) { return s1.unwrap() != s2; }
 }
diff --git a/test/codec/common_code.cc b/test/codec/common_code.cc
index 28b31c8..d659e5a 100644
--- a/test/codec/common_code.cc
+++ b/test/codec/common_code.cc
@@ -88,9 +88,15 @@ TEST(CommonCode, operators) {
     std::cout.setstate(std::ios::failbit); // hide std::cout content
     std::cout << "TEST OUTPUT -> " << CommonCode(TEST_CODE) << std::endl; // ostream test
     std::cout.clear();
-    EXPECT_EQ(CommonCode(TEST_CODE), TEST_CODE); // operator `==`
-    EXPECT_EQ(CommonCode(TEST_CODE), CommonCode(TEST_CODE)); // operator `==`
     EXPECT_EQ((uint64_t)CommonCode(TEST_CODE), TEST_CODE); // convert as uint64_t
+
+    EXPECT_EQ(TEST_CODE, CommonCode(TEST_CODE)); // uint64_t == CommonCode
+    EXPECT_EQ(CommonCode(TEST_CODE), TEST_CODE); // CommonCode == uint64_t
+    EXPECT_EQ(CommonCode(TEST_CODE), CommonCode(TEST_CODE)); // CommonCode == CommonCode
+
+    EXPECT_NE(TEST_CODE + 1, CommonCode(TEST_CODE)); // uint64_t != CommonCode
+    EXPECT_NE(CommonCode(TEST_CODE), TEST_CODE + 1); // CommonCode != uint64_t
+    EXPECT_NE(CommonCode(TEST_CODE), CommonCode::unsafe_create(TEST_CODE + 1)); // CommonCode != CommonCode
 }
 
 TEST(CommonCode, code_convert) {
diff --git a/test/codec/raw_code.cc b/test/codec/raw_code.cc
index dd0245c..058be4b 100644
--- a/test/codec/raw_code.cc
+++ b/test/codec/raw_code.cc
@@ -36,9 +36,15 @@ TEST(RawCode, operators) {
     std::cout.setstate(std::ios::failbit); // hide std::cout content
     std::cout << "TEST OUTPUT" << std::endl << RawCode(TEST_CODE); // ostream test
     std::cout.clear();
-    EXPECT_EQ(RawCode(TEST_CODE), TEST_CODE); // operator `==`
-    EXPECT_EQ(RawCode(TEST_CODE), RawCode(TEST_CODE)); // operator `==`
     EXPECT_EQ((uint64_t)RawCode(TEST_CODE), TEST_CODE); // convert as uint64_t
+
+    EXPECT_EQ(TEST_CODE, RawCode(TEST_CODE)); // uint64_t == RawCode
+    EXPECT_EQ(RawCode(TEST_CODE), TEST_CODE); // RawCode == uint64_t
+    EXPECT_EQ(RawCode(TEST_CODE), RawCode(TEST_CODE)); // RawCode == RawCode
+
+    EXPECT_NE(TEST_CODE + 1, RawCode(TEST_CODE)); // uint64_t != RawCode
+    EXPECT_NE(RawCode(TEST_CODE), TEST_CODE + 1); // RawCode != uint64_t
+    EXPECT_NE(RawCode(TEST_CODE), RawCode::unsafe_create(TEST_CODE + 1)); // RawCode != RawCode
 }
 
 TEST(RawCode, code_convert) {
diff --git a/test/codec/short_code.cc b/test/codec/short_code.cc
index 8d70047..4c118b7 100644
--- a/test/codec/short_code.cc
+++ b/test/codec/short_code.cc
@@ -109,9 +109,15 @@ TEST(ShortCode, operators) {
     std::cout.setstate(std::ios::failbit); // hide std::cout content
     std::cout << "TEST OUTPUT -> " << ShortCode(TEST_CODE) << std::endl; // ostream test
     std::cout.clear();
-    EXPECT_EQ(ShortCode(TEST_CODE), TEST_CODE); // operator `==`
-    EXPECT_EQ(ShortCode(TEST_CODE), ShortCode(TEST_CODE)); // operator `==`
     EXPECT_EQ((uint32_t)ShortCode(TEST_CODE), TEST_CODE); // convert as uint64_t
+
+    EXPECT_EQ(TEST_CODE, ShortCode(TEST_CODE)); // uint32_t == ShortCode
+    EXPECT_EQ(ShortCode(TEST_CODE), TEST_CODE); // ShortCode == uint32_t
+    EXPECT_EQ(ShortCode(TEST_CODE), ShortCode(TEST_CODE)); // ShortCode == ShortCode
+
+    EXPECT_NE(TEST_CODE + 1, ShortCode(TEST_CODE)); // uint32_t != ShortCode
+    EXPECT_NE(ShortCode(TEST_CODE), TEST_CODE + 1); // ShortCode != uint32_t
+    EXPECT_NE(ShortCode(TEST_CODE), ShortCode::unsafe_create(TEST_CODE + 1)); // ShortCode != ShortCode
 }
 
 TEST(ShortCode, code_convert) {