This habilitation paper is devoted to the fundamental role of rings and modules in algebraic coding theory and cryptology. It is organized as follows:
Chapter 1: Rings, weight functions and modulation schemes (Classes of finite Dedekind rings, Weights and their symmetry groups, Modulation schemes);
Chapter 2: Algebraic coding theory over rings (Characterization of cyclic codes, Monomial representation of homogeneous isometries, Characterization of Hamming isometries);
Chapter 3: Efficient decoding of linear codes over chain rings (\(p\)-adic representations, Decoding free codes, Application to quaternary Reed-Muller codes);
Chapter 4: Residue class codes under selected weights (The quaternary Preparata codes and their decodings, On \(\mathbb{Z}_4\) and \(\mathbb{Z}_9\) lifts of the Golay codes and their decoding, Construction of a ternary \((36,3^{12},15)\)-code;
Chapter 5: Linear codes and matrix rings (Morita equivalence and its metric continuation, Matrix representations of linear codes); and
Chapter 6: Secret sharing over partially ordered sets (Control schemes and homogeneity, Information rates and perfection, Construction of perfect control schemes, An example).
Note that the author has published some of these results in English [M. Greferath and S. E. Schmidt, Linear codes and rings of matrices, Lect. Notes Comput. Sci. 1719, 160-169 (1999; Zbl 0989.94029)] and M. Greferath, Discrete Math. 177, 273-277 (1997; Zbl 0886.94014)].