Information on Result #1021554
Linear OOA(567, large, F5, 3, 6), 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(541, 2796201, F5, 3, 6) (dual of [(2796201, 3), 8388562, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(541, large, F5, 6) (dual of [large, large−41, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(541, large, F5, 6) (dual of [large, large−41, 7]-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(567, large, F5, 3, 5) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(567, large, F5, 3, 4) | [i] | ||
| 3 | Linear OOA(567, large, F5, 3, 3) | [i] | ||
| 4 | Linear OOA(570, large, F5, 3, 6) | [i] | NRT-Code Embedding in Larger Space | |
| 5 | Linear OOA(573, large, F5, 3, 6) | [i] | ||
| 6 | Linear OOA(576, large, F5, 3, 6) | [i] | ||
| 7 | Linear OOA(579, large, F5, 3, 6) | [i] | ||
| 8 | Linear OOA(582, large, F5, 3, 6) | [i] | ||
| 9 | Linear OOA(585, large, F5, 3, 6) | [i] | ||
| 10 | Linear OOA(588, large, F5, 3, 6) | [i] | ||
| 11 | Linear OOA(591, large, F5, 3, 6) | [i] | ||
| 12 | Linear OOA(594, large, F5, 3, 6) | [i] | ||
| 13 | Linear OOA(597, large, F5, 3, 6) | [i] | ||
| 14 | Linear OOA(5100, large, F5, 3, 6) | [i] | ||
| 15 | Linear OOA(5106, large, F5, 3, 6) | [i] | ||
| 16 | Linear OOA(5109, large, F5, 3, 6) | [i] | ||
| 17 | Linear OOA(5112, large, F5, 3, 6) | [i] | ||
| 18 | Linear OOA(5115, large, F5, 3, 6) | [i] | ||
| 19 | Linear OOA(5118, large, F5, 3, 6) | [i] | ||
| 20 | Linear OOA(5121, large, F5, 3, 6) | [i] | ||
| 21 | Linear OOA(5124, large, F5, 3, 6) | [i] | ||
| 22 | Linear OOA(5127, large, F5, 3, 6) | [i] | ||
| 23 | Linear OOA(5130, large, F5, 3, 6) | [i] | ||
| 24 | Linear OOA(5133, large, F5, 3, 6) | [i] | ||
| 25 | Linear OOA(5139, large, F5, 3, 6) | [i] | ||
| 26 | Linear OOA(5142, large, F5, 3, 6) | [i] | ||
| 27 | Linear OOA(5145, large, F5, 3, 6) | [i] | ||
| 28 | Linear OOA(5148, large, F5, 3, 6) | [i] | ||
| 29 | Linear OOA(569, large, F5, 3, 6) | [i] | OOA Duplication | |
| 30 | Linear OOA(567, 8388602, F5, 9, 6) (dual of [(8388602, 9), 75497351, 7]-NRT-code) | [i] | OOA Stacking with Additional Row | |