On 3-dimensional MRD codes of type \(\langle X^{q^t},X+\delta X^{q^{2t}},G(X) \rangle \)

The article investigates 3-dimensional Maximum Rank Distance (MRD) codes, a type of error-correcting code with applications in cryptography and network coding. It explores the mathematical properties of these codes, including their relationship with scattered polynomials and algebraic varieties. The authors delve into the classification of exceptional MRD codes, which are particularly interesting due to their potential for cryptographic applications. The study employs techniques from algebraic geometry over finite fields to prove the non-existence of certain exceptional MRD codes, contributing to the broader understanding of these codes and their applications in coding theory.