Minimum distance of linear codes and the $\alpha$-invariant

Abstract

The simple interpretation of the minimum distance of a linear code obtained by De Boer and Pellikaan, and later refined by the second author, is further developed through the study of various finitely generated graded modules. We use the methods of commutative/homological algebra to find connections between the minimum distance and the $\alpha$-invariant of such modules.

12 pages