Massimiliano Sala edited section_Bytes_The_polynomials_in__.tex  about 6 years ago

Commit id: 4032ccc7d25fc56571cd3d592245f65c24d248d7

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This set is finite, because the degree of its polynomials is at most $n-1$, and again  it actually contains all polynomials with degree at most $n-1$  $$  A \,=\, \{ 0,1,x,x+1,\ldots,x^{n-1},x^{n-1}+1,\ldots,x^{n-1}+x^{n-2}+\cdots+x+1\} \. \,.  $$  Also in this general setting, we can sum and multiply. The sum is obvious, the multiplication  may require some divisions by $g$ before we can arrive at a small-degree polynomial.