Name
Title | ||
|---|---|---|
Optimal constant weight covering codes and nonuniform group divisible 3-designs with block size four |
Abstract | ||
|---|---|---|
Let K q (n, w, t, d) be the minimum size of a code over Z q of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this article, we determine K q (n, 4, 3, 1) for all n 驴 4, q = 3, 4 or q = 2 m + 1 with m 驴 2, leaving the only case (q, n) = (3, 5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames, which play a crucial role in the recursive constructions of group divisible 3-designs similar to that of candelabra systems in the constructions of 3-wise balanced designs. As an application of this approach, several new infinite classes of nonuniform group divisible 3-designs with block size four are also constructed. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s10623-011-9499-8 | Des. Codes Cryptography |
Keywords | Field | DocType |
Constant weight covering code,Group divisible,t,-covering,Group divisible,t,-design,H-frame,Primary 05B40,94B65,05C35 | Block size,Discrete mathematics,Combinatorics,Hamming distance,Code word,Construction method,Code (cryptography),Mathematics,Recursion | Journal |
Volume | Issue | ISSN |
62 | 2 | 0925-1022 |
Citations | PageRank | References |
1 | 0.40 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiande Zhang | 1 | 52 | 15.19 |
| Hui Zhang | 2 | 1 | 0.40 |
| Gennian Ge | 3 | 904 | 95.51 |