Linear recurring arrays, linear systems and multidimensional cyclic codes over quasi-Frobenius rings
In this paper, authors define and characterize multidimensional cyclic codes and their dual codes over quasi-Frobenius rings as a generalization of the undimensional approach of \textit{A. R. Calderbank} and \textit{J. A. Sloane} [Des. Codes Cryptography 6, No. 1, 21--35 (1995; Zbl 0848.94020)], \textit{P. Kanwar} and \textit{S. R. Lopez-Permouth} [Finite Fields Appl. 3, No. 4 , 334--352 (1997; Zbl 1055.94541)], \textit{Z. Wan} [Algebra Colloq. 6, No. 3, 291--304 (1999; Zbl 1022.94022)] and \textit{G. H. Norton} and \textit{A. Salagean} [Appl. Algebra Eng. Commun. Comput. 10, No. 6, 489--506 (2000; Zbl 0963.94042)]. Exploring the quasi-Frobenius ring property and its associated duality theory, they work on the relation between polynomial modules of Arrays and their associated inverse system in a quasi-Frobenius module over an Artinian ring. The paper is well presented with correct citations and gives a very good contribution to cyclic codes over finite rings.
scientific article; zbMATH DE number 2073425