Information on Result #695769
Linear OA(2733, 743, F27, 15) (dual of [743, 710, 16]-code), using construction X applied to Ce(14) ⊂ Ce(9) based on
- linear OA(2729, 729, F27, 15) (dual of [729, 700, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2719, 729, F27, 10) (dual of [729, 710, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(2733, 722, F27, 2, 15) (dual of [(722, 2), 1411, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (18, 33, 722)-net over F27 | [i] | ||