# Windmill Generators A generalization and an observation of how many there are

Conference paper

First Online:

## Abstract

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.

Download
to read the full conference paper text

## References

- [1]European Broadcasting Union: “Specification of the systems of the MAC/packet family)”, Tech 3258-E (Brussels: EBU technical centre), 1986.Google Scholar
- [2]A. Lempel, W.L. Eastman, “High speed generation of maximal length sequences”, IEEE Trans. on Comput., Vol. C-20, (1971), pp. 227–229.CrossRefGoogle Scholar
- [3]A.C. Arvillias, D.G. Maritsas, “Combinational logicfree realisations for high-speed m-sequence generation”, Electronics Letters, Vo1.13, no.17, (1977), pp. 500–502.CrossRefGoogle Scholar
- [4]F. Surböck, H. Weinrichter, “Interlacing properties of shift-register sequences with generator polynomials irreducible over GF(
*p*)”, IEEE Trans. on Inform. Theory, Vol. IT-24, (1978), pp. 386–389.CrossRefGoogle Scholar - [5]B.J.M. Smeets.
*On Linear Recurring Sequences*, PhD dissertation, University of Lund, 1987.Google Scholar - [6]R. Lidl, H. Niederreiter,
*Finite Fields*, Encyclopedia of Mathematics and its Applications, Vol. 20, Addison-Wesley, Reading, Mass, 1983.Google Scholar - [7]S.D. Cohen, “Windmill polynomials over fields of characteristic two”, preprint.Google Scholar
- [8]E.R. Berlekamp,
*Algebraic Coding Theory*, McGraw-Hill, New York, 1968.zbMATHGoogle Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1988