I understand construction of irreducible polynomials over finite fields is a non trivial problem. Can anyone please refer me to good resources regarding constructive approaches of irreducible polynomials?
Also a perspective of how construction of irreducible polynomial will help to understand other branches of mathematics such as coding theory, cryptography,etc., will be very helpful.
I am currently reading Lidl's 'Finite Fields' and found the conditions regarding the same problem a bit absurd looking and not very intuitive, (specially chapher 3, section 3 part). Can I have better ways to comprehend those results?
Added by mixedmath
The OP indicated in the comments that the parts of this book that are relevant are theorems 3.36 and 3.37. For ease, I display what is freely available here. Unfortunately, there is no theorem 3.36. But there is an example 3.36:
And the part of the theorem that we can access:
The rest is not included in the preview.
Edit:
I found this http://www.math.leidenuniv.nl/~hwl/PUBLICATIONS/1986a/art.pdf , in this paper the authors give an algorithm for constructing irreducible polynomials, but my mathematical background does not permit me to understand the paper fully, still if someone please explains the steps in the first algorithm with an example i will be glad.
Specifically the fourth step of the first algorithm remains unclear to me.