Information on Result #699271
Linear OA(8177, 531472, F81, 24) (dual of [531472, 531395, 25]-code), using construction X applied to Ce(23) ⊂ Ce(15) based on
- linear OA(8170, 531441, F81, 24) (dual of [531441, 531371, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(817, 31, F81, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,81)), using
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), using
- Reed–Solomon code RS(74,81) [i]
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), 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(8177, 443304, F81, 2, 24) (dual of [(443304, 2), 886531, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8177, 443304, F81, 3, 24) (dual of [(443304, 3), 1329835, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(8177, 443304, F81, 4, 24) (dual of [(443304, 4), 1773139, 25]-NRT-code) | [i] | ||
| 4 | Digital (53, 77, 443304)-net over F81 | [i] | ||
| 5 | Linear OOA(8177, 265736, F81, 2, 24) (dual of [(265736, 2), 531395, 25]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8177, 177157, F81, 3, 24) (dual of [(177157, 3), 531394, 25]-NRT-code) | [i] | ||
| 7 | Linear OOA(8177, 132868, F81, 4, 24) (dual of [(132868, 4), 531395, 25]-NRT-code) | [i] | ||