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In this paper, we count the number of matrices whose rows generate different$\mathbb{Z}_2\mathbb{Z}_8$ additive codes. This is a natural generalization ofthe well known Gaussian numbers that count the number of matrices whose rowsgenerate vector spaces with particular dimension over finite fields. Due tothis similarity we name this numbers as Mixed Generalized Gaussian Numbers(MGN). The MGN formula by specialization leads to the well known formula forthe number of binary codes and the number of codes over $\mathbb{Z}_8,$ and foradditive $\mathbb{Z}_2\mathbb{Z}_4$ codes. Also, we conclude by some propertiesand examples of the MGN numbers that provide a good source for new numbersequences that are not listed in The On-Line Encyclopedia of Integer Sequences.

Counting The Generator Matrices of $\mathbb{Z}_{2}\mathbb{Z}_{8}$-Codes