Information on Result #735853
Linear OA(12822, 2097285, F128, 7) (dual of [2097285, 2097263, 8]-code), using (u, u+v)-construction based on
- linear OA(1283, 130, F128, 3) (dual of [130, 127, 4]-code or 130-arc in PG(2,128) or 130-cap in PG(2,128)), using
- linear OA(12819, 2097155, F128, 7) (dual of [2097155, 2097136, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(6) ⊂ Ce(5) [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(12822, 2097285, F128, 2, 7) (dual of [(2097285, 2), 4194548, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12822, 2097285, F128, 3, 7) (dual of [(2097285, 3), 6291833, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(12822, 2097285, F128, 4, 7) (dual of [(2097285, 4), 8389118, 8]-NRT-code) | [i] | ||
| 4 | Digital (15, 22, 2097285)-net over F128 | [i] | ||
| 5 | Linear OOA(12822, 1048642, F128, 2, 7) (dual of [(1048642, 2), 2097262, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12822, 699095, F128, 3, 7) (dual of [(699095, 3), 2097263, 8]-NRT-code) | [i] | ||