Research Projects

Over the past 30 years, researchers have made significant contributions to error-correcting codes, focusing on complete algebraic structures of linear codes over finite commutative Frobenius rings and computing their Hamming distance. However, there is a lack of focus on computing the Lee distance, which is crucial for finding good codes over finite fields through Gray maps. The Lee metric is significant for applications such as multidimensional burst error correction, VLSI implementation, DNA-based storage, and post-quantum cryptosystems. Finding good classes of Lee metric codes with a fast decoding algorithm is an important step. The mathematical theory of quantum error-correcting codes has helped construct a large family of quantum codes, including stabilizer codes. The method of obtaining stabilizer codes via Hermitian self-orthogonal codes over GF(4) is well-studied. The objective is to explore the possibility of developing the theory of quantum error-correcting codes in the Lee metric setting and obtaining stabilizer codes via Lee self-orthogonal codes over GF(4).