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    Counting The Generator Matrices of Z2Z8\mathbb{Z}_{2}\mathbb{Z}_{8}-Codes

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    In this paper, we count the number of matrices whose rows generate different Z2Z8\mathbb{Z}_2\mathbb{Z}_8 additive codes. This is a natural generalization of the well known Gaussian numbers that count the number of matrices whose rows generate vector spaces with particular dimension over finite fields. Due to this similarity we name this numbers as Mixed Generalized Gaussian Numbers (MGN). The MGN formula by specialization leads to the well known formula for the number of binary codes and the number of codes over Z8,\mathbb{Z}_8, and for additive Z2Z4\mathbb{Z}_2\mathbb{Z}_4 codes. Also, we conclude by some properties and examples of the MGN numbers that provide a good source for new number sequences that are not listed in The On-Line Encyclopedia of Integer Sequences
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