Information on Result #1193622
Digital (108, 120, 2806083)-net over F9, using net defined by OOA based on linear OOA(9120, 2806083, F9, 15, 12) (dual of [(2806083, 15), 42091125, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9120, 5612167, F9, 3, 12) (dual of [(5612167, 3), 16836381, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9120, 5612168, F9, 3, 12) (dual of [(5612168, 3), 16836384, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(930, 19766, F9, 3, 6) (dual of [(19766, 3), 59268, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(94, 82, F9, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
- linear OOA(926, 19684, F9, 3, 6) (dual of [(19684, 3), 59026, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(926, 59052, F9, 6) (dual of [59052, 59026, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(926, 59054, F9, 6) (dual of [59054, 59028, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(926, 59049, F9, 6) (dual of [59049, 59023, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(921, 59049, F9, 5) (dual of [59049, 59028, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(926, 59054, F9, 6) (dual of [59054, 59028, 7]-code), using
- OOA 3-folding [i] based on linear OA(926, 59052, F9, 6) (dual of [59052, 59026, 7]-code), using
- (u, u+v)-construction [i] based on
- 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(930, 19766, F9, 3, 6) (dual of [(19766, 3), 59268, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(9120, 5612168, F9, 3, 12) (dual of [(5612168, 3), 16836384, 13]-NRT-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 (228, 240, 5612166)-net over F3 | [i] | Trace Code for Nets | |