Information on Result #878614
Linear OOA(12853, 1048579, F128, 2, 18) (dual of [(1048579, 2), 2097105, 19]-NRT-code), using OOA 2-folding based on linear OA(12853, 2097158, F128, 18) (dual of [2097158, 2097105, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12853, 2097159, F128, 18) (dual of [2097159, 2097106, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ 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(12863, 1048729, F128, 2, 18) (dual of [(1048729, 2), 2097395, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12853, 738708, F128, 3, 18) (dual of [(738708, 3), 2216071, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12853, 738708, F128, 4, 18) (dual of [(738708, 4), 2954779, 19]-NRT-code) | [i] | ||
| 4 | Digital (35, 53, 738708)-net over F128 | [i] | ||