An Algorithm for Finding Self-Orthogonal and Self-Dual Codes Over Gaussian and Eisenstein Integer Residue Rings Via Chinese Remainder Theorem

A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this which closed under the action constant multiplication by integers. In paper, we define dual codes for and rings, consider construction self-dual codes. Because, uniqueness prime element decomposition holds same way as one-variable polynomial rings finite fields rational ring, provide efficient method generator matrices using that moduli. As numerical examples, enumerate construct actual moduli when matrix size two.