Information on Result #1193628
Digital (112, 124, 2973350)-net over F9, using net defined by OOA based on linear OOA(9124, 2973350, F9, 15, 12) (dual of [(2973350, 15), 44600126, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9124, 5946701, F9, 3, 12) (dual of [(5946701, 3), 17839979, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(934, 354299, F9, 3, 6) (dual of [(354299, 3), 1062863, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(934, 1062897, F9, 6) (dual of [1062897, 1062863, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(934, 1062898, F9, 6) (dual of [1062898, 1062864, 7]-code), using
- trace code [i] based on linear OA(8117, 531449, F81, 6) (dual of [531449, 531432, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(817, 8, F81, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,81)), using
- dual of repetition code with length 8 [i]
- linear OA(811, 8, F81, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- Reed–Solomon code RS(80,81) [i]
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(8117, 531449, F81, 6) (dual of [531449, 531432, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(934, 1062898, F9, 6) (dual of [1062898, 1062864, 7]-code), using
- OOA 3-folding [i] based on linear OA(934, 1062897, F9, 6) (dual of [1062897, 1062863, 7]-code), using
- linear OOA(990, 5592402, F9, 3, 12) (dual of [(5592402, 3), 16777116, 13]-NRT-code), using
- trace code [i] based on linear OOA(8145, 2796201, F81, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- trace code [i] based on linear OOA(8145, 2796201, F81, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- linear OOA(934, 354299, F9, 3, 6) (dual of [(354299, 3), 1062863, 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 (236, 248, 5946700)-net over F3 | [i] | Trace Code for Nets | |