Information on Result #695182
Linear OA(2749, 19698, F27, 16) (dual of [19698, 19649, 17]-code), using construction X applied to Ce(15) ⊂ Ce(11) based on
- linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2734, 19683, F27, 12) (dual of [19683, 19649, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), 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(2749, 18787, F27, 2, 16) (dual of [(18787, 2), 37525, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (33, 49, 18787)-net over F27 | [i] | ||
| 3 | Linear OOA(2749, 9849, F27, 2, 16) (dual of [(9849, 2), 19649, 17]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2749, 2462, F27, 16, 16) (dual of [(2462, 16), 39343, 17]-NRT-code) | [i] | OA Folding and Stacking | |