Information on Result #694851
Linear OA(2771, 531455, F27, 18) (dual of [531455, 531384, 19]-code), using construction X applied to Ce(17) ⊂ Ce(14) based on
- linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2757, 531441, F27, 15) (dual of [531441, 531384, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(272, 14, F27, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), 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(2771, 478382, F27, 2, 18) (dual of [(478382, 2), 956693, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 71, 478382)-net over F27 | [i] | ||
| 3 | Linear OOA(2771, 265727, F27, 2, 18) (dual of [(265727, 2), 531383, 19]-NRT-code) | [i] | OOA Folding | |