Information on Result #694842
Linear OA(27108, 531456, F27, 28) (dual of [531456, 531348, 29]-code), using construction X applied to Ce(27) ⊂ Ce(23) based on
- linear OA(27105, 531441, F27, 28) (dual of [531441, 531336, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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 OA(27107, 531455, F27, 27) (dual of [531455, 531348, 28]-code) | [i] | Truncation | |
| 2 | Linear OOA(27108, 315438, F27, 2, 28) (dual of [(315438, 2), 630768, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (80, 108, 315438)-net over F27 | [i] | ||
| 4 | Linear OOA(27108, 265728, F27, 2, 28) (dual of [(265728, 2), 531348, 29]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(27108, 37961, F27, 28, 28) (dual of [(37961, 28), 1062800, 29]-NRT-code) | [i] | OA Folding and Stacking | |