Information on Result #694865
Linear OA(27109, 531461, F27, 28) (dual of [531461, 531352, 29]-code), using construction X applied to Ce(27) ⊂ Ce(22) 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(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(274, 20, F27, 4) (dual of [20, 16, 5]-code or 20-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(27109, 358071, F27, 2, 28) (dual of [(358071, 2), 716033, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (81, 109, 358071)-net over F27 | [i] | ||
| 3 | Linear OOA(27109, 265730, F27, 2, 28) (dual of [(265730, 2), 531351, 29]-NRT-code) | [i] | OOA Folding | |