Information on Result #1202252
Digital (51, 62, 2799481)-net over F81, using net defined by OOA based on linear OOA(8162, 2799481, F81, 15, 11) (dual of [(2799481, 15), 41992153, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8162, 5598963, F81, 3, 11) (dual of [(5598963, 3), 16796827, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8162, 5598964, F81, 3, 11) (dual of [(5598964, 3), 16796830, 12]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(814, 6562, F81, 3, 3) (dual of [(6562, 3), 19682, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(814, 6562, F81, 2, 3) (dual of [(6562, 2), 13120, 4]-NRT-code), using
- 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(814, 6562, F81, 3, 3) (dual of [(6562, 3), 19682, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8162, 5598964, F81, 3, 11) (dual of [(5598964, 3), 16796830, 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 (113, 124, 5598962)-net over F9 | [i] | Trace Code for Nets | |