Information on Result #735714
Linear OA(12861, 2097284, F128, 18) (dual of [2097284, 2097223, 19]-code), using (u, u+v)-construction based on
- linear OA(1289, 129, F128, 9) (dual of [129, 120, 10]-code or 129-arc in PG(8,128)), using
- extended Reed–Solomon code RSe(120,128) [i]
- the expurgated narrow-sense BCH-code C(I) with length 129 | 1282−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [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(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(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(17) ⊂ Ce(16) [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(12861, 2097284, F128, 2, 18) (dual of [(2097284, 2), 4194507, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12861, 2097284, F128, 3, 18) (dual of [(2097284, 3), 6291791, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(12861, 2097284, F128, 4, 18) (dual of [(2097284, 4), 8389075, 19]-NRT-code) | [i] | ||
| 4 | Digital (43, 61, 2097284)-net over F128 | [i] | ||
| 5 | Linear OOA(12861, 1048642, F128, 2, 18) (dual of [(1048642, 2), 2097223, 19]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12861, 699094, F128, 3, 18) (dual of [(699094, 3), 2097221, 19]-NRT-code) | [i] | ||