Information on Result #1021990
Linear OOA(763, large, F7, 3, 6), using generalized (u, u+v)-construction based on
- linear OOA(78, 960800, F7, 3, 2) (dual of [(960800, 3), 2882392, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(78, 960800, F7, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
- appending kth column [i] based on linear OA(78, 960800, F7, 2) (dual of [960800, 960792, 3]-code), using
- Hamming code H(8,7) [i]
- appending kth column [i] based on linear OA(78, 960800, F7, 2) (dual of [960800, 960792, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(78, 960800, F7, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
- linear OOA(713, 3843202, F7, 3, 3) (dual of [(3843202, 3), 11529593, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(713, 6120100, F7, 3, 3) (dual of [(6120100, 3), 18360287, 4]-NRT-code), using
- linear OOA(742, 3843202, F7, 3, 6) (dual of [(3843202, 3), 11529564, 7]-NRT-code), using
- trace code [i] based on linear OOA(4921, 1921601, F49, 3, 6) (dual of [(1921601, 3), 5764782, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4917, 5764801, F49, 5) (dual of [5764801, 5764784, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(4921, 5764805, F49, 6) (dual of [5764805, 5764784, 7]-code), using
- OOA 3-folding [i] based on linear OA(4921, 5764803, F49, 6) (dual of [5764803, 5764782, 7]-code), using
- trace code [i] based on linear OOA(4921, 1921601, F49, 3, 6) (dual of [(1921601, 3), 5764782, 7]-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(763, large, F7, 3, 5) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(763, large, F7, 3, 4) | [i] | ||
| 3 | Linear OOA(763, large, F7, 3, 3) | [i] | ||
| 4 | Linear OOA(766, large, F7, 3, 6) | [i] | NRT-Code Embedding in Larger Space | |
| 5 | Linear OOA(769, large, F7, 3, 6) | [i] | ||
| 6 | Linear OOA(778, large, F7, 3, 6) | [i] | ||
| 7 | Linear OOA(781, large, F7, 3, 6) | [i] | ||
| 8 | Linear OOA(784, large, F7, 3, 6) | [i] | ||
| 9 | Linear OOA(787, large, F7, 3, 6) | [i] | ||
| 10 | Linear OOA(790, large, F7, 3, 6) | [i] | ||
| 11 | Linear OOA(796, large, F7, 3, 6) | [i] | ||
| 12 | Linear OOA(799, large, F7, 3, 6) | [i] | ||
| 13 | Linear OOA(7108, large, F7, 3, 6) | [i] | ||
| 14 | Linear OOA(763, 8388602, F7, 9, 6) (dual of [(8388602, 9), 75497355, 7]-NRT-code) | [i] | OOA Stacking with Additional Row | |