Information on Result #735734
Linear OA(12857, 2097284, F128, 17) (dual of [2097284, 2097227, 18]-code), using (u, u+v)-construction based on
- linear OA(1288, 129, F128, 8) (dual of [129, 121, 9]-code or 129-arc in PG(7,128)), using
- extended Reed–Solomon code RSe(121,128) [i]
- linear OA(12849, 2097155, F128, 17) (dual of [2097155, 2097106, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(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(16) ⊂ Ce(15) [i] based on
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 | Linear OOA(12857, 2097284, F128, 2, 17) (dual of [(2097284, 2), 4194511, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12857, 2097284, F128, 3, 17) (dual of [(2097284, 3), 6291795, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(12857, 2097284, F128, 4, 17) (dual of [(2097284, 4), 8389079, 18]-NRT-code) | [i] | ||
| 4 | Digital (40, 57, 2097284)-net over F128 | [i] | ||
| 5 | Linear OOA(12857, 1048642, F128, 2, 17) (dual of [(1048642, 2), 2097227, 18]-NRT-code) | [i] | OOA Folding | |