Classification of a Class of A2MDS codes and Application in Cryptography Algorithms

Abstract

This manuscript delves into q-ary linear codes, particularly focusing on their classification and properties. A q-ary linear code with parameters [n, k, n – k+1] is known as an MDS code. A q-ary linear code characterized by [n, k, n − k − (i − 1)] parameters is called an AiMDS code. An A2MDS code whose dual is also an A2MDS code is called an N2MDS code. This manuscript presents a comprehensive classification of most binary N2MDS codes. Additionally, we unveil a distinctive sub-class within A2MDS codes, notable for its intriguing access structure in code-based secret-sharing, promising novel avenues for secure information distribution.