Information on Result #1193626
Digital (110, 122, 2973348)-net over F9, using net defined by OOA based on linear OOA(9122, 2973348, F9, 15, 12) (dual of [(2973348, 15), 44600098, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(9122, 5946697, F9, 3, 12) (dual of [(5946697, 3), 17839969, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9122, 5946698, F9, 3, 12) (dual of [(5946698, 3), 17839972, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(932, 354296, F9, 3, 6) (dual of [(354296, 3), 1062856, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(932, 1062888, F9, 6) (dual of [1062888, 1062856, 7]-code), using
- trace code [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [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(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- trace code [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- OOA 3-folding [i] based on linear OA(932, 1062888, F9, 6) (dual of [1062888, 1062856, 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(932, 354296, F9, 3, 6) (dual of [(354296, 3), 1062856, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(9122, 5946698, F9, 3, 12) (dual of [(5946698, 3), 17839972, 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 (232, 244, 5946696)-net over F3 | [i] | Trace Code for Nets | |