Information on Result #695239
Linear OA(2786, 19711, F27, 28) (dual of [19711, 19625, 29]-code), using construction X applied to Ce(27) ⊂ Ce(19) based on
- linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(277, 28, F27, 7) (dual of [28, 21, 8]-code or 28-arc in PG(6,27)), using
- extended Reed–Solomon code RSe(21,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
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 OA(2787, 19712, F27, 28) (dual of [19712, 19625, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2785, 19710, F27, 27) (dual of [19710, 19625, 28]-code) | [i] | Truncation | |
| 3 | Linear OOA(2786, 19386, F27, 2, 28) (dual of [(19386, 2), 38686, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (58, 86, 19386)-net over F27 | [i] | ||
| 5 | Linear OA(2787, 19713, F27, 28) (dual of [19713, 19626, 29]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(2786, 9855, F27, 2, 28) (dual of [(9855, 2), 19624, 29]-NRT-code) | [i] | OOA Folding | |