Information on Result #699755
Linear OA(12830, 2097163, F128, 10) (dual of [2097163, 2097133, 11]-code), using construction X applied to Ce(9) ⊂ Ce(6) based on
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), 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(1653, 2097163, S16, 10) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3242, 2097163, S32, 10) | [i] | ||
| 3 | OA(6435, 2097163, S64, 10) | [i] | ||
| 4 | Linear OOA(12830, 1289797, F128, 2, 10) (dual of [(1289797, 2), 2579564, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12830, 1289797, F128, 3, 10) (dual of [(1289797, 3), 3869361, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(12830, 1289797, F128, 4, 10) (dual of [(1289797, 4), 5159158, 11]-NRT-code) | [i] | ||
| 7 | Digital (20, 30, 1289797)-net over F128 | [i] | ||
| 8 | Linear OOA(12830, 1048581, F128, 2, 10) (dual of [(1048581, 2), 2097132, 11]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12830, 699054, F128, 3, 10) (dual of [(699054, 3), 2097132, 11]-NRT-code) | [i] | ||
| 10 | Linear OOA(12830, 524290, F128, 4, 10) (dual of [(524290, 4), 2097130, 11]-NRT-code) | [i] | ||
| 11 | Linear OOA(12830, 419432, F128, 10, 10) (dual of [(419432, 10), 4194290, 11]-NRT-code) | [i] | OA Folding and Stacking | |