  A systematic method is presented for the construction and classification of
algebras of gauge transformations for arbitrary high rank tensor gauge fields.
For every tensor gauge field of a given rank, the gauge transformation will be
stated, in a generic way, via an ansatz that contains all the possible terms,
with arbitrary coefficients and the maximum number of tensor gauge functions.
The requirement for the closure of the algebra will prove to be restrictive,
but, nevertheless, leave a variety of choices. Properly adjusting the values of
the initial coefficients and imposing restrictions on the gauge functions, one
can, one the one hand, recover all the, so far, analysed algebras and on the
other, construct new ones. The presentation of a brand new algebra for tensor
gauge transformations is the central result of this article.
