🤖 AI Summary
This work addresses the systematic construction of reversible linear codes, reversible self-dual codes, and reversible DNA codes by proposing a unified matrix concatenation framework based on involution matrices over finite commutative rings. By integrating the matrix product approach with DNA code mapping techniques, the study not only resolves an open problem posed by Oztas et al., but also corrects and improves upon certain of their results, thereby establishing a cohesive theory for constructing reversible codes. The proposed method yields a broad class of generator matrices with favorable parameters, enabling the successful construction of various novel reversible linear and DNA codes, significantly expanding both the scope and performance of existing constructions.
📝 Abstract
In this paper, we develop a generalized framework for constructing reversible linear, reversible self dual and reversible DNA codes using a matrix-theoretic approach based on involutory matrices. The proposed concatenation scheme gives a large class of generator matrices and yields codes with good parameters. The construction is carried out at the level of linear codes and then extended to DNA codes. Using a matrix product approach, we provide a unified method for analysis and proof. Further, we resolve an open problem raised by Oztas et.al. and also we correct and improve some results of them.