Distance Distributions and Energy of Designs in Hamming Spaces

Authors

  • Peter Boyvalenkov Institute of Mathematics and Informatics Bulgarian Academy of Sciences Acad G. Bonchev Str., bl. 8 1113, Sofia, Bulgaria
  • Tanya Marinova Faculty of Mathematics and Informatics Sofia University 5, James Bourchier Blvd 1164 Sofia, Bulgaria
  • Maya Stoyanova Faculty of Mathematics and Informatics Sofia University 5, James Bourchier Blvd 1164 Sofia, Bulgaria
  • Mila Sukalinska Faculty of Mathematics and Natural Sciences South-Western University, 66, I. Michailov Str. Blagoevgrad, Bulgaria

Keywords:

Designs in Hamming Spaces, Distance Distribution, Energy

Abstract

We obtain new combinatorial upper and lower bounds for the
potential energy of designs in q-ary Hamming space. Combined with results
on reducing the number of all feasible distance distributions of such designs
this gives reasonable good bounds. We compute and compare our lower
bounds to recently obtained universal lower bounds. Some examples in the
binary case are considered.

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Published

2022-04-13

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Section

Articles