Information on Result #876712
Linear OOA(8159, 265724, F81, 2, 20) (dual of [(265724, 2), 531389, 21]-NRT-code), using OOA 2-folding based on linear OA(8159, 531448, F81, 20) (dual of [531448, 531389, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [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(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(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(8171, 265840, F81, 2, 20) (dual of [(265840, 2), 531609, 21]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8159, 224842, F81, 3, 20) (dual of [(224842, 3), 674467, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8159, 224842, F81, 4, 20) (dual of [(224842, 4), 899309, 21]-NRT-code) | [i] | ||
| 4 | Digital (39, 59, 224842)-net over F81 | [i] | ||