Information on Result #695204
Linear OA(2759, 19702, F27, 19) (dual of [19702, 19643, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
- linear OA(2755, 19683, F27, 19) (dual of [19683, 19628, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2740, 19683, F27, 14) (dual of [19683, 19643, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(274, 19, F27, 4) (dual of [19, 15, 5]-code or 19-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(2759, 19702, F27, 2, 19) (dual of [(19702, 2), 39345, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (40, 59, 19702)-net over F27 | [i] | ||
| 3 | Linear OOA(2759, 9851, F27, 2, 19) (dual of [(9851, 2), 19643, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2759, 2189, F27, 19, 19) (dual of [(2189, 19), 41532, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |