Information on Result #1050836
Linear OOA(817, 3281, F81, 4, 4) (dual of [(3281, 4), 13117, 5]-NRT-code), using OA 2-folding and stacking based on linear OA(817, 6562, F81, 4) (dual of [6562, 6555, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(815, 6561, F81, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [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(8136, 2100431, F81, 4, 8) (dual of [(2100431, 4), 8401688, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8132, 136142, F81, 4, 9) (dual of [(136142, 4), 544536, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(8140, 2100431, F81, 4, 9) (dual of [(2100431, 4), 8401684, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(8181, 4200862, F81, 4, 13) (dual of [(4200862, 4), 16803367, 14]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 5 | Linear OOA(8177, 4200862, F81, 4, 12) (dual of [(4200862, 4), 16803371, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(8177, 4197581, F81, 4, 13) (dual of [(4197581, 4), 16790247, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(8173, 4197581, F81, 4, 12) (dual of [(4197581, 4), 16790251, 13]-NRT-code) | [i] | ||
| 8 | Digital (3, 7, 3281)-net over F81 | [i] | Net Defined by OOA | |