Counting Z2Z4Z8-additive codes

Abstract

In Algebraic Coding Theory, all linear codes can be described by generator matrices. Any linear code has different generator matrices. It is important to find the number of the generator matrices for the construction of these codes. In this paper, we study Z(2)Z(4)Z(8)-additive codes, which are an extension of Z(2)Z(4)-additive codes. We count the number of arbitrary Z(2)Z(4)Z(8)-additive codes. Then we investigate connections to Z(2) Z(4) and Z(2)Z(8)-additive codes with Z(2)Z(4)Z(8)-additive codes, and give some illustrative examples.