Information on Result #876714
Linear OOA(8161, 265728, F81, 2, 20) (dual of [(265728, 2), 531395, 21]-NRT-code), using OOA 2-folding based on linear OA(8161, 531456, F81, 20) (dual of [531456, 531395, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8146, 531441, F81, 16) (dual of [531441, 531395, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), 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(8161, 265728, F81, 3, 20) (dual of [(265728, 3), 797123, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8161, 265728, F81, 4, 20) (dual of [(265728, 4), 1062851, 21]-NRT-code) | [i] | ||
| 3 | Digital (41, 61, 265728)-net over F81 | [i] | ||