Information on Result #695766
Linear OA(2739, 743, F27, 18) (dual of [743, 704, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(2735, 729, F27, 18) (dual of [729, 694, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2725, 729, F27, 13) (dual of [729, 704, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(274, 14, F27, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,27)), using
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
- Reed–Solomon code RS(23,27) [i]
- discarding factors / shortening the dual code based on linear OA(274, 27, F27, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,27)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2739, 649, F27, 2, 18) (dual of [(649, 2), 1259, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (21, 39, 649)-net over F27 | [i] | ||