Information on Result #699703
Linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code), using construction X applied to Ce(15) ⊂ Ce(14) based on
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | OA(1681, 2097155, S16, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3265, 2097155, S32, 16) | [i] | ||
| 3 | OA(6454, 2097155, S64, 16) | [i] | ||
| 4 | Linear OA(12854, 2097284, F128, 16) (dual of [2097284, 2097230, 17]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12855, 2097305, F128, 16) (dual of [2097305, 2097250, 17]-code) | [i] | ||
| 6 | Linear OA(12856, 2097307, F128, 16) (dual of [2097307, 2097251, 17]-code) | [i] | ||
| 7 | Linear OA(12857, 2097347, F128, 16) (dual of [2097347, 2097290, 17]-code) | [i] | ||
| 8 | Linear OA(12858, 2097413, F128, 16) (dual of [2097413, 2097355, 17]-code) | [i] | ||
| 9 | Linear OA(12859, 2097539, F128, 16) (dual of [2097539, 2097480, 17]-code) | [i] | ||
| 10 | Linear OA(12860, 2097542, F128, 16) (dual of [2097542, 2097482, 17]-code) | [i] | ||
| 11 | Linear OOA(12846, 1048577, F128, 2, 16) (dual of [(1048577, 2), 2097108, 17]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(12846, 699051, F128, 3, 16) (dual of [(699051, 3), 2097107, 17]-NRT-code) | [i] | ||