Irreducible Coefficient Relations
The distribution of coefficients of irreducible polynomials over GF(2) has long been a subject of interest for coding theorists and researchers in related fields. In this paper, we prove that the only affine relations holding on these coefficients are essentially trivial. We also give an extension of this result to arbitrary finite fields GF(q), where “affine” is replaced by “degree at most q-1”.
- 3.Golomb, S.W., et al.: Shift Register Sequences. Holden-Day, Inc., San Francisco (1967), 2nd edn. Aegean Park Press (1982)Google Scholar
- 5.Lidl, R., Niederreiter, H.: Finite fields, 2nd edn. Encyclopedia of Mathematics and its Applications, vol. 20. Cambridge University Press, Cambridge (1997); With a foreword by P. M. CohnGoogle Scholar