Name
Abstract | ||
|---|---|---|
Let C be a linear [n,k,d]-code over GF(q) with k⩾2. If s=n-k+1-d denotes the defect of C, then by the Griesmer bound, d⩽(s+1)q. Now, for obvious reasons, we are interested in codes of given defect s for which the minimum distance is maximal, i.e., d=(s+1)q. We classify up to formal equivalence all such linear codes over GF(q). Remember that two codes over GF(q) are formally equivalent if they have the same weight distribution. It turns out that for k⩾3 such codes exist only in dimension 3 and 4 with the ternary extended Golay code, the ternary dual Golay code, and the binary even-weight code as exceptions. In dimension 4 they are related to ovoids in PG(3,q) except the binary extended Hamming code, and in dimension 3 to maximal arcs in PG(2,q) |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1109/18.681331 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
weight distribution,minimum distance,binary even-weight code,formal equivalence,golay code,mmd code,ternary dual golay code,linear code,1-d denotes,obvious reason,hamming code,galois fields,hamming codes | Discrete mathematics,Combinatorics,Constant-weight code,Block code,Ternary Golay code,Cyclic code,Linear code,Reed–Muller code,Binary Golay code,Hamming bound,Mathematics | Journal |
Volume | Issue | ISSN |
44 | 4 | 0018-9448 |
Citations | PageRank | References |
10 | 0.83 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. Faldum | 1 | 10 | 0.83 |
| W. Willems | 2 | 44 | 5.12 |