Information on Result #2769508
Linear OOA(399, large, F3, 4, 4), using strength reduction based on linear OOA(399, large, F3, 4, 7), using
- (u, u+v)-construction [i] based on
- linear OOA(33, 4, F3, 4, 3) (dual of [(4, 4), 13, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;13,3) [i]
- linear OOA(396, 8388602, F3, 4, 7) (dual of [(8388602, 4), 33554312, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(396, large, F3, 3, 7), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(315, 2796201, F3, 3, 2) (dual of [(2796201, 3), 8388588, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(315, 7174453, F3, 3, 2) (dual of [(7174453, 3), 21523344, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(315, 7174453, F3, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- appending kth column [i] based on linear OA(315, 7174453, F3, 2) (dual of [7174453, 7174438, 3]-code), using
- Hamming code H(15,3) [i]
- appending kth column [i] based on linear OA(315, 7174453, F3, 2) (dual of [7174453, 7174438, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(315, 7174453, F3, 2, 2) (dual of [(7174453, 2), 14348891, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(315, 7174453, F3, 3, 2) (dual of [(7174453, 3), 21523344, 3]-NRT-code), using
- linear OOA(320, 2796201, F3, 3, 3) (dual of [(2796201, 3), 8388583, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, 3713023, F3, 3, 3) (dual of [(3713023, 3), 11139049, 4]-NRT-code), using
- linear OOA(361, 2796201, F3, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- linear OOA(315, 2796201, F3, 3, 2) (dual of [(2796201, 3), 8388588, 3]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(396, large, F3, 3, 7), using
- linear OOA(33, 4, F3, 4, 3) (dual of [(4, 4), 13, 4]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3100, large, F3, 4, 4) | [i] | OOA Duplication | |
| 2 | Linear OOA(3101, large, F3, 4, 4) | [i] | ||
| 3 | Linear OOA(3102, large, F3, 4, 4) | [i] | ||