TY - JOUR
T1 - Improved upper bounds on sizes of codes
AU - Mounits, Beniamin
AU - Etzion, Tuvi
AU - Litsyn, Simon
N1 - Funding Information:
Manuscript received May 20, 2000. The work of T. Etzion was supported in part by the Israeli Science Foundation under Grant 88/99. The work of S. Litsyn was supported in part by the Binational Science Foundation under Grant 1999099. B. Mounits is with the Department of Mathematics, Technion–Israel Institute of Technology, Haifa 32000, Israel (e-mail: [email protected]). T. Etzion is with the Department of Computer Science, Technion–Israel Institute of Technology, Haifa 32000, Israel (e-mail: [email protected]). S. Litsyn is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Tel-Aviv, Israel (e-mail: [email protected]). Communicated by P. Solé, Associate Editor for Coding Theory. Publisher Item Identifier S 0018-9448(02)01939-9.
PY - 2002/4
Y1 - 2002/4
N2 - Let A(n, d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n, d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n, d) for n ≤ 28 are improved.
AB - Let A(n, d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n, d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n, d) for n ≤ 28 are improved.
KW - A(n, d)
KW - Holes
KW - Johnson bound
KW - Linear programming bound
UR - http://www.scopus.com/inward/record.url?scp=0036539258&partnerID=8YFLogxK
U2 - 10.1109/18.992776
DO - 10.1109/18.992776
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AN - SCOPUS:0036539258
SN - 0018-9448
VL - 48
SP - 880
EP - 886
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
ER -