Information on Result #1202250
Digital (50, 61, 2796241)-net over F81, using net defined by OOA based on linear OOA(8161, 2796241, F81, 15, 11) (dual of [(2796241, 15), 41943554, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8161, 5592483, F81, 3, 11) (dual of [(5592483, 3), 16777388, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8161, 5592484, F81, 3, 11) (dual of [(5592484, 3), 16777391, 12]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(813, 82, F81, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;243,81) [i]
- linear OOA(8117, 2796201, F81, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8117, 4194301, F81, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(8117, 4194301, F81, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- linear OOA(8141, 2796201, F81, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- linear OOA(813, 82, F81, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8161, 5592484, F81, 3, 11) (dual of [(5592484, 3), 16777391, 12]-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 (111, 122, 5592482)-net over F9 | [i] | Trace Code for Nets | |