Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN EXTREMAL PROBLEM APPLIED TO THE RUDIN-SHAPIRO POLYNOMIALS

  • Published : 1998.03.01

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Abstract

Given a Unimodular polynomial P of degree N$\geq$1, the exteremal problem for ${\gamma}$ =max{｜P(eit)｜:0 $\leq$t$\leq$2$\pi$} satisfies ${\gamma}$$\leq$C{{{{ SQRT { N+1} where C is a universal constant. Here we show that C < 2+{{{{ whenever N is fixed and P has the coefficients of a Rudin-Shapiro polynomial.

Keywords

References

  1. Group synchronizing of binary digital systems in communication theory R.H.Barker
  2. MS thesis M.I.T. Extremal problems for polynomials and power series H.S.Shapiro
  3. Iranian Journal of Science and Technology v.20 no.2 An estimate on the correlation coefficients of the Rudin-Shapiro polynomials M.Taghavi
  4. Korean Journal of Computational and Applied Mathematics v.4 no.1 Upper bounds for the autocorrelation coefficients of the Rudin-Shapiro polynomials M.Taghavi
  5. Sequences with small correlation in "error correcting codes" R.Turyn;H.Mann(ed.)