Information on Result #2485043
Linear OOA(3220, large, F3, 2, 7), using 69 times NRT-code embedding in larger space based on linear OOA(382, 8388602, F3, 2, 7) (dual of [(8388602, 2), 16777122, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(321, 7426048, F3, 2, 3) (dual of [(7426048, 2), 14852075, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(321, 7426048, F3, 3) (dual of [7426048, 7426027, 4]-code or 7426048-cap in PG(20,3)), using
- linear OOA(361, 4194301, F3, 2, 7) (dual of [(4194301, 2), 8388541, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(361, 8388602, F3, 7) (dual of [8388602, 8388541, 8]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- OOA 2-folding [i] based on linear OA(361, 8388602, F3, 7) (dual of [8388602, 8388541, 8]-code), using
- linear OOA(321, 7426048, F3, 2, 3) (dual of [(7426048, 2), 14852075, 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(3221, large, F3, 2, 7) | [i] | OOA Duplication | |