Improved Semidefinite Programming Bound on Sizes of Codes
SCIE
SCOPUS
- Title
- Improved Semidefinite Programming Bound on Sizes of Codes
- Authors
- Kim, HK; Toan, PT
- Date Issued
- 2013-11
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Abstract
- Let A(n,d) (respectively A(n,d,w) ) be the maximum possible number of codewords in a binary code (respectively, binary constant-weight w code) of length n and minimum Hamming distance at least d. By adding new linear constraints to Schrijver's semidefinite programming bound, which is obtained from block-diagonalizing the Terwilliger algebra of the Hamming cube, we obtain two new upper bounds on A(n,d) , namely A(18,8) <= 71 and A(19,8) <= 131. Twenty three new upper bounds on A(n,d,w) for n <= 28 are also obtained by a similar way.
- Keywords
- Binary codes; binary constant-weight codes; linear programming; semidefinite programming; upper bound; CONSTANT-WEIGHT CODES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/14519
- DOI
- 10.1109/TIT.2013.2277714
- ISSN
- 0018-9448
- Article Type
- Article
- Citation
- IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 59, no. 11, page. 7337 - 7345, 2013-11
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