On codes over product of finite chain rings
1Department of Mathematics, Malayer University, Malayer, 65719, Iran
2Department of Mathematics, Bu Ali Sina University, Hamedan, 65175 Iran
2Department of Mathematics, Bu Ali Sina University, Hamedan, 65175 Iran
Sigma J Eng Nat Sci 2023; 41(1): 145-155 DOI: 10.14744/sigma.2023.00014
Abstract
In this paper, codes over the direct product of two finite commutative chain rings are studied. The standard form of the parity-check matrix is determined. The structure of self-dual codes is described. A distance preserving Gray map from the direct product of chain rings to a finite field is defined. Two upper bounds on minimum distance are obtained.
Keywords: MDS Codes; Self-Dual Codes; Chain Rings
