Information on Result #699273
Linear OA(8165, 531472, F81, 20) (dual of [531472, 531407, 21]-code), using construction X applied to Ce(19) ⊂ Ce(11) 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(8134, 531441, F81, 12) (dual of [531441, 531407, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(8165, 531472, F81, 2, 20) (dual of [(531472, 2), 1062879, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8165, 531472, F81, 3, 20) (dual of [(531472, 3), 1594351, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(8165, 531472, F81, 4, 20) (dual of [(531472, 4), 2125823, 21]-NRT-code) | [i] | ||
| 4 | Digital (45, 65, 531472)-net over F81 | [i] | ||
| 5 | Linear OOA(8165, 265736, F81, 2, 20) (dual of [(265736, 2), 531407, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8165, 177157, F81, 3, 20) (dual of [(177157, 3), 531406, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(8165, 132868, F81, 4, 20) (dual of [(132868, 4), 531407, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(8165, 53147, F81, 20, 20) (dual of [(53147, 20), 1062875, 21]-NRT-code) | [i] | OA Folding and Stacking | |