Information on Result #1193742
Digital (109, 122, 2798389)-net over F9, using net defined by OOA based on linear OOA(9122, 2798389, F9, 15, 13) (dual of [(2798389, 15), 41975713, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9122, 5596779, F9, 3, 13) (dual of [(5596779, 3), 16790215, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(924, 4377, F9, 3, 6) (dual of [(4377, 3), 13107, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(924, 13131, F9, 6) (dual of [13131, 13107, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(924, 13132, F9, 6) (dual of [13132, 13108, 7]-code), using
- trace code [i] based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(5) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(8112, 6566, F81, 6) (dual of [6566, 6554, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(924, 13132, F9, 6) (dual of [13132, 13108, 7]-code), using
- OOA 3-folding [i] based on linear OA(924, 13131, F9, 6) (dual of [13131, 13107, 7]-code), using
- linear OOA(998, 5592402, F9, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- linear OOA(924, 4377, F9, 3, 6) (dual of [(4377, 3), 13107, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
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 (231, 244, 5596778)-net over F3 | [i] | Trace Code for Nets | |