Enumeration of some matrices and free linear codes over commutative finite local rings

Abstract

Let R be a commutative finite local ring. Two enumeration problems over R are presented. We enumerate the matrices over R with a given McCoy rank and a given number of rows of single unit, and the free linear codes over R which have a given rank and a given number of vectors of single unit.

Keywords

• mccoy rank
• free linear code
• local ring
• 15a03
• 94b05