On the Zeros of the Askey–Wilson Polynomials, with Applications to Coding Theory
Copyright policy )On the Zeros of the Askey–Wilson Polynomials, with Applications to Coding Theory
In a symmetric association scheme that is (P and Q)-polynomial, the P and Q eigenmatrices are given by balanced \({}_ 4\Phi_ 3\) Askey-Wilson polynomials. In this paper, the parameters of the Askey-Wilson polynomial are classified so that its zeros are not contained in its spectrum. These results, together with theorems of Biggs and Delsarte, imply the nonexistence of perfect codes and tight designs in the classical association schemes of type \(A_ N\), \(B_ N\), \(C_ N\), \(D_ N\) and the affine matrix schemes.
- University of Minnesota Morris United States
- University of Minnesota United States
- University of Minnesota System United States
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), tight designs, perfect codes, Askey-Wilson polynomials, association schemes
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), tight designs, perfect codes, Askey-Wilson polynomials, association schemes
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).35 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!