Information on Result #1194062
Digital (54, 72, 1459)-net over F9, using net defined by OOA based on linear OOA(972, 1459, F9, 18, 18) (dual of [(1459, 18), 26190, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(972, 13131, F9, 18) (dual of [13131, 13059, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(972, 13132, F9, 18) (dual of [13132, 13060, 19]-code), using
- trace code [i] based on linear OA(8136, 6566, F81, 18) (dual of [6566, 6530, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(8136, 6566, F81, 18) (dual of [6566, 6530, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(972, 13132, F9, 18) (dual of [13132, 13060, 19]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (55, 73, 1459)-net over F9 | [i] | Net Duplication | |
| 2 | Digital (56, 74, 1459)-net over F9 | [i] | ||