Information on Result #876766
Linear OOA(8163, 265726, F81, 2, 21) (dual of [(265726, 2), 531389, 22]-NRT-code), using OOA 2-folding based on linear OA(8163, 531452, F81, 21) (dual of [531452, 531389, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(812, 11, F81, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), 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(8163, 265726, F81, 3, 21) (dual of [(265726, 3), 797115, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8163, 265726, F81, 4, 21) (dual of [(265726, 4), 1062841, 22]-NRT-code) | [i] | ||
| 3 | Digital (42, 63, 265726)-net over F81 | [i] | ||