On the size of maximal binary codes with 2, 3, and 4 distances

Alexander Barg, Alexey Glazyrin, Wei Jiun Kao, Ching Yi Lai, Pin Chieh Tseng, Wei Hsuan Yu

Research output: Contribution to journalArticlepeer-review

Abstract

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths n ≥ 6 as well as the exact size of maximal binary constant weight codes with 2, 3, and 4 distances for several values of the weight and for all but small lengths.

Original languageEnglish
Article number#7
JournalCombinatorial Theory
Volume4
Issue number1
DOIs
StatePublished - 2024

Keywords

  • Delsarte inequalities
  • Erdӧs–Ko–Rado
  • Johnson space

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