Properties of Codes with Empty Kernel

Abstract

In 2010, J. Berstel, D. Perrin and C. Felice first proposed the definition of a code with empty kernel and obtained the nature theorem of associated with group codes in the paper “On the groups of codes with empty kernelâ€. In this paper, we present sufficient and necessary conditions to depict codes with empty kernel. We also give some methods to construct codes with empty kernel and maximal codes with empty kernel.