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Partial sums of binomials, intersecting numbers, and the excess bound in Rosenbloom–Tsfasman space

  • André G. Castoldi
  • Emerson L. do Monte Carmelo
  • Robson da SilvaEmail author
Article
  • 1 Downloads

Abstract

In this work, the sphere-covering bound on covering codes in Rosenbloom–Tsfasman spaces (RT spaces) is improved by generalizing the excess counting method. The approach focuses on studying the parity of a Rosenbloom–Tsfasman sphere (RT sphere) and the parity of the intersection of two RT spheres. We connect the parity of an RT sphere with partial sums of binomial coefficients and p-adic valuation of binomial coefficients. The intersection number of RT spaces is introduced and we determinate its parity under some conditions. Numerical applications of the method are discussed.

Keywords

Rosenbloom–Tsfasman metric Covering code Bounds on code Sum of binomials Congruence 

Mathematics Subject Classification

94B25 05A10 05A19 06A06 

Notes

Acknowledgements

The authors would like to thank the anonymous referees for their suggestions that greatly improved this paper.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Institute of Science and TechnologyFederal University of São PauloSão José dos CamposBrazil
  2. 2.Department of MathematicsFederal University of TechnologyParanáBrazil
  3. 3.Department of MathematicsState University of MaringáMaringáBrazil

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