diff --git a/dump/src/reader/compat/v5_to_v6.rs b/dump/src/reader/compat/v5_to_v6.rs
index 2fe99e2af..3f360e329 100644
--- a/dump/src/reader/compat/v5_to_v6.rs
+++ b/dump/src/reader/compat/v5_to_v6.rs
@@ -260,7 +260,7 @@ impl From<v5::ResponseError> for v6::ResponseError {
             "invalid_index_uid" => v6::Code::InvalidIndexUid,
             "invalid_min_word_length_for_typo" => v6::Code::InvalidMinWordLengthForTypo,
             "invalid_state" => v6::Code::InvalidState,
-            "primary_key_inference_failed" => v6::Code::MissingPrimaryKey,
+            "primary_key_inference_failed" => v6::Code::NoPrimaryKeyCandidateFound,
             "index_primary_key_already_exists" => v6::Code::PrimaryKeyAlreadyPresent,
             "max_fields_limit_exceeded" => v6::Code::MaxFieldsLimitExceeded,
             "missing_document_id" => v6::Code::MissingDocumentId,
diff --git a/meilisearch-types/src/error.rs b/meilisearch-types/src/error.rs
index e8b108595..846b690b0 100644
--- a/meilisearch-types/src/error.rs
+++ b/meilisearch-types/src/error.rs
@@ -126,7 +126,8 @@ pub enum Code {
 
     // invalid state error
     InvalidState,
-    MissingPrimaryKey,
+    NoPrimaryKeyCandidateFound,
+    MultiplePrimaryKeyCandidatesFound,
     PrimaryKeyAlreadyPresent,
 
     MaxFieldsLimitExceeded,
@@ -211,9 +212,13 @@ impl Code {
             // invalid state error
             InvalidState => ErrCode::internal("invalid_state", StatusCode::INTERNAL_SERVER_ERROR),
             // thrown when no primary key has been set
-            MissingPrimaryKey => {
-                ErrCode::invalid("primary_key_inference_failed", StatusCode::BAD_REQUEST)
+            NoPrimaryKeyCandidateFound => {
+                ErrCode::invalid("index_primary_key_no_candidate_found", StatusCode::BAD_REQUEST)
             }
+            MultiplePrimaryKeyCandidatesFound => ErrCode::invalid(
+                "index_primary_key_multiple_candidates_found",
+                StatusCode::BAD_REQUEST,
+            ),
             // error thrown when trying to set an already existing primary key
             PrimaryKeyAlreadyPresent => {
                 ErrCode::invalid("index_primary_key_already_exists", StatusCode::BAD_REQUEST)
@@ -405,7 +410,10 @@ impl ErrorCode for milli::Error {
                     UserError::InvalidDocumentId { .. } | UserError::TooManyDocumentIds { .. } => {
                         Code::InvalidDocumentId
                     }
-                    UserError::MissingPrimaryKey => Code::MissingPrimaryKey,
+                    UserError::NoPrimaryKeyCandidateFound => Code::NoPrimaryKeyCandidateFound,
+                    UserError::MultiplePrimaryKeyCandidatesFound { .. } => {
+                        Code::MultiplePrimaryKeyCandidatesFound
+                    }
                     UserError::PrimaryKeyCannotBeChanged(_) => Code::PrimaryKeyAlreadyPresent,
                     UserError::SortRankingRuleMissing => Code::Sort,
                     UserError::InvalidFacetsDistribution { .. } => Code::BadRequest,