Windmill Generators A generalization and an observation of how many there are
The windmill technique has several practical advantageous over other techniques for high-speed generation or blockwise generation of pn-sequences. In this paper we generalize previous results by showing that if f(t)=α(t v) − β(t −v )t L is the minimal polynomial of a pn-sequence, then the sequence can be generated by a windmill generator. For L = 1, ...127, and ν = 4, 8, 16 such that L ≡ ±3 mod 8 no irreducible polynomials f(t) were found. When L ≡ ±1 mod 8 the number of primitive f(t)’s was found to be approximately twice the expected number.
- European Broadcasting Union: “Specification of the systems of the MAC/packet family)”, Tech 3258-E (Brussels: EBU technical centre), 1986.Google Scholar
- B.J.M. Smeets. On Linear Recurring Sequences, PhD dissertation, University of Lund, 1987.Google Scholar
- R. Lidl, H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Applications, Vol. 20, Addison-Wesley, Reading, Mass, 1983.Google Scholar
- S.D. Cohen, “Windmill polynomials over fields of characteristic two”, preprint.Google Scholar