1999/10/31 by A. Ashikhmin, Alexei Ashikhmin, Alexander Barg +6 · 1 citation
Computer Science · Engineering · Mathematics · #05E30 #33C45 #94A24 #94B27 #Coding theory and cryptography #Combinatorics (math.CO) #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.CO #math.IT #msc:05E30 #msc:33C45 #msc:94A24 #msc:94B27
paper · pdf · doi:10.48550/arxiv.math/9910175
11 pages
arxiv created 1999/10/31 · openalex publication_date 1999/10/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In recent works of the authors the applicability of the method was extended to cover a wider range of problems in coding and information theory. In this paper we present a general framework for the method which includes previous results as particular cases. We explain how this generalization leads to new asymptotic bounds on the performance of codes in binary-input memoryless channels and the Gaussian channel, which improve the results of Shannon et al. of 1959-67, and to a number of other results in combinatorial coding theory.