COUNTING THE GENERATOR MATRICES OF Z2Z8-CODES
Abstract
In this paper, we count the number of matrices whose rows generate different Z2Z8additive codes. This is a natural generalization of thewell 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). By specialization of MGN formula the well known formula forthe number of binary codes and the number of codes over Z8, and for additive Z2Z4codes are easily derived. Also, we conclude by some properties andexamples 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
Keywords
Gaussian numbers, Mixed Generalized Gaussian Numbers, NewSequences
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