Information on Result #1192336
Digital (103, 123, 209717)-net over F8, using net defined by OOA based on linear OOA(8123, 209717, F8, 20, 20) (dual of [(209717, 20), 4194217, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8123, 2097170, F8, 20) (dual of [2097170, 2097047, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8123, 2097176, F8, 20) (dual of [2097176, 2097053, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(8123, 2097176, F8, 20) (dual of [2097176, 2097053, 21]-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 (104, 124, 209717)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (105, 125, 209717)-net over F8 | [i] | ||