Information on Result #907122
Linear OOA(12816, large, F128, 2, 4), using generalized (u, u+v)-construction based on
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1280, s, F128, 2, 0) for arbitrarily large s, using
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1280, 1048577, F128, 2, 0) (dual of [(1048577, 2), 2097154, 1]-NRT-code) (see above)
- linear OOA(1281, 1048577, F128, 2, 1) (dual of [(1048577, 2), 2097153, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 2, 1) for arbitrarily large s, using
- linear OOA(1281, 1048577, F128, 2, 1) (dual of [(1048577, 2), 2097153, 2]-NRT-code) (see above)
- linear OOA(1284, 1048577, F128, 2, 2) (dual of [(1048577, 2), 2097150, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- Hamming code H(4,128) [i]
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- linear OOA(12810, 1048577, F128, 2, 4) (dual of [(1048577, 2), 2097144, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OOA 2-folding [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-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(12816, large, F128, 2, 3) | [i] | Strength Reduction for OOAs | |
2 | Linear OOA(12818, large, F128, 2, 4) | [i] | NRT-Code Embedding in Larger Space | |
3 | Linear OOA(12822, large, F128, 2, 4) | [i] | ||
4 | Linear OOA(12824, large, F128, 2, 4) | [i] | ||
5 | Linear OOA(12826, large, F128, 2, 4) | [i] | ||
6 | Linear OOA(12828, large, F128, 2, 4) | [i] | ||
7 | Linear OOA(12830, large, F128, 2, 4) | [i] | ||
8 | Linear OOA(12832, large, F128, 2, 4) | [i] | ||
9 | Linear OOA(12834, large, F128, 2, 4) | [i] | ||
10 | Linear OOA(12836, large, F128, 2, 4) | [i] | ||
11 | Linear OOA(12838, large, F128, 2, 4) | [i] | ||
12 | Linear OOA(12840, large, F128, 2, 4) | [i] | ||
13 | Linear OOA(12842, large, F128, 2, 4) | [i] | ||
14 | Linear OOA(12844, large, F128, 2, 4) | [i] | ||
15 | Linear OOA(12846, large, F128, 2, 4) | [i] | ||
16 | Linear OOA(12848, large, F128, 2, 4) | [i] | ||
17 | Linear OOA(12850, large, F128, 2, 4) | [i] | ||
18 | Linear OOA(12852, large, F128, 2, 4) | [i] | ||
19 | Linear OOA(12854, large, F128, 2, 4) | [i] | ||
20 | Linear OOA(12856, large, F128, 2, 4) | [i] | ||
21 | Linear OOA(12858, large, F128, 2, 4) | [i] | ||
22 | Linear OOA(12860, large, F128, 2, 4) | [i] | ||
23 | Linear OOA(12862, large, F128, 2, 4) | [i] | ||
24 | Linear OOA(12864, large, F128, 2, 4) | [i] | ||
25 | Linear OOA(12866, large, F128, 2, 4) | [i] | ||
26 | Linear OOA(12868, large, F128, 2, 4) | [i] | ||
27 | Linear OOA(12870, large, F128, 2, 4) | [i] | ||
28 | Linear OOA(12872, large, F128, 2, 4) | [i] | ||
29 | Linear OOA(12874, large, F128, 2, 4) | [i] | ||
30 | Linear OOA(12876, large, F128, 2, 4) | [i] | ||
31 | Linear OOA(12878, large, F128, 2, 4) | [i] | ||
32 | Linear OOA(12817, large, F128, 2, 4) | [i] | OOA Duplication | |
33 | Linear OOA(12816, 8388602, F128, 3, 4) (dual of [(8388602, 3), 25165790, 5]-NRT-code) | [i] | OOA Stacking with Additional Row | |
34 | Linear OOA(12816, 8388602, F128, 4, 4) (dual of [(8388602, 4), 33554392, 5]-NRT-code) | [i] |