Information on Result #1021545
Linear OOA(577, large, F5, 3, 7), using generalized (u, u+v)-construction based on
- linear OOA(51, 2441406, F5, 3, 1) (dual of [(2441406, 3), 7324217, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(51, s, F5, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(51, s, F5, 3, 1) for arbitrarily large s, using
- linear OOA(510, 2441406, F5, 3, 2) (dual of [(2441406, 3), 7324208, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(510, 2441406, F5, 2, 2) (dual of [(2441406, 2), 4882802, 3]-NRT-code), using
- appending kth column [i] based on linear OA(510, 2441406, F5, 2) (dual of [2441406, 2441396, 3]-code), using
- Hamming code H(10,5) [i]
- appending kth column [i] based on linear OA(510, 2441406, F5, 2) (dual of [2441406, 2441396, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(510, 2441406, F5, 2, 2) (dual of [(2441406, 2), 4882802, 3]-NRT-code), using
- linear OOA(515, 2796201, F5, 3, 3) (dual of [(2796201, 3), 8388588, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(515, 3050325, F5, 3, 3) (dual of [(3050325, 3), 9150960, 4]-NRT-code), using
- linear OOA(551, 2796201, F5, 3, 7) (dual of [(2796201, 3), 8388552, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(551, large, F5, 7) (dual of [large, large−51, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(551, large, F5, 7) (dual of [large, large−51, 8]-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(577, large, F5, 3, 6) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(577, large, F5, 3, 5) | [i] | ||
| 3 | Linear OOA(577, large, F5, 3, 4) | [i] | ||
| 4 | Linear OOA(577, large, F5, 3, 3) | [i] | ||
| 5 | Linear OOA(580, large, F5, 3, 7) | [i] | NRT-Code Embedding in Larger Space | |
| 6 | Linear OOA(583, large, F5, 3, 7) | [i] | ||
| 7 | Linear OOA(586, large, F5, 3, 7) | [i] | ||
| 8 | Linear OOA(589, large, F5, 3, 7) | [i] | ||
| 9 | Linear OOA(592, large, F5, 3, 7) | [i] | ||
| 10 | Linear OOA(595, large, F5, 3, 7) | [i] | ||
| 11 | Linear OOA(598, large, F5, 3, 7) | [i] | ||
| 12 | Linear OOA(5101, large, F5, 3, 7) | [i] | ||
| 13 | Linear OOA(5104, large, F5, 3, 7) | [i] | ||
| 14 | Linear OOA(5107, large, F5, 3, 7) | [i] | ||
| 15 | Linear OOA(5110, large, F5, 3, 7) | [i] | ||
| 16 | Linear OOA(5113, large, F5, 3, 7) | [i] | ||
| 17 | Linear OOA(5116, large, F5, 3, 7) | [i] | ||
| 18 | Linear OOA(5119, large, F5, 3, 7) | [i] | ||
| 19 | Linear OOA(5122, large, F5, 3, 7) | [i] | ||
| 20 | Linear OOA(5125, large, F5, 3, 7) | [i] | ||
| 21 | Linear OOA(5128, large, F5, 3, 7) | [i] | ||
| 22 | Linear OOA(5131, large, F5, 3, 7) | [i] | ||
| 23 | Linear OOA(5134, large, F5, 3, 7) | [i] | ||
| 24 | Linear OOA(5137, large, F5, 3, 7) | [i] | ||
| 25 | Linear OOA(5143, large, F5, 3, 7) | [i] | ||
| 26 | Linear OOA(5146, large, F5, 3, 7) | [i] | ||
| 27 | Linear OOA(5149, large, F5, 3, 7) | [i] | ||
| 28 | Linear OOA(579, large, F5, 3, 7) | [i] | OOA Duplication | |
| 29 | Linear OOA(577, 8388602, F5, 9, 7) (dual of [(8388602, 9), 75497341, 8]-NRT-code) | [i] | OOA Stacking with Additional Row | |