representing binary finite fields in ASN.1
For a binary field $\mathbb{F}_{2^m}$, the polynomial necessarily has degree $m$ (otherwise the field would not have cardinal $2^m$), and its least significant coefficient must be $1$, not $0$ (otherwise the polynomial would not be irreducible, and the field would not be a field).

Therefore, for $\mathbb{F}_{2^{193}}$, if the polynomial is a trinomial, then it is already known that is is $x^{193}+x^j+1$ for some integer $1&lt;j&lt;193$. Only that integer $j$ needs to be encoded, which is why you only have one INTEGER. In other words, when trying to encode $x^{193}+x^{15}+1$, only the "15" needs to be encoded; the "193" and the "0" are implicit.

Similarly, for a pentanomial, you only have to encode three exponents, since the two extremes (0 and the field size) are implicit.