Information on Result #876300
Linear OOA(8115, 3281, F81, 2, 8) (dual of [(3281, 2), 6547, 9]-NRT-code), using OOA 2-folding based on linear OA(8115, 6562, F81, 8) (dual of [6562, 6547, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 6563, F81, 8) (dual of [6563, 6548, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
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(8119, 3363, F81, 2, 8) (dual of [(3363, 2), 6707, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8120, 3381, F81, 2, 8) (dual of [(3381, 2), 6742, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(8176, 4197582, F81, 2, 16) (dual of [(4197582, 2), 8395088, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(8180, 4197582, F81, 2, 17) (dual of [(4197582, 2), 8395084, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(8115, 2982, F81, 3, 8) (dual of [(2982, 3), 8931, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(8115, 2982, F81, 4, 8) (dual of [(2982, 4), 11913, 9]-NRT-code) | [i] | ||
| 7 | Digital (7, 15, 2982)-net over F81 | [i] | ||