Information on Result #689170
Linear OA(999, 531451, F9, 19) (dual of [531451, 531352, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(985, 531441, F9, 16) (dual of [531441, 531356, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
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(999, 284294, F9, 2, 19) (dual of [(284294, 2), 568489, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(999, 284294, F9, 3, 19) (dual of [(284294, 3), 852783, 20]-NRT-code) | [i] | ||
| 3 | Digital (80, 99, 284294)-net over F9 | [i] | ||
| 4 | Linear OOA(999, 265725, F9, 2, 19) (dual of [(265725, 2), 531351, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(999, 177150, F9, 3, 19) (dual of [(177150, 3), 531351, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(999, 59050, F9, 19, 19) (dual of [(59050, 19), 1121851, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |