Abstract
We study the upper bounds for A(n, d), the maximum size of codewords with length n and Hamming distance at least d. Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound A(n, d). We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver’s semidefinite programming bounds on A(n, d). In particular, we improve the semidefinite programming bounds on A(18, 4) to 6551.
| Original language | English |
|---|---|
| Pages (from-to) | 3241-3262 |
| Number of pages | 22 |
| Journal | Designs, Codes, and Cryptography |
| Volume | 91 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 2023 |
Keywords
- Binary codes
- Distance distribution
- Semidefinite program
- Terwilliger algebra
- Weight enumeration