Information on Result #699756
Linear OA(12827, 2097163, F128, 9) (dual of [2097163, 2097136, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(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(1648, 2097163, S16, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3238, 2097163, S32, 9) | [i] | ||
| 3 | OA(6432, 2097163, S64, 9) | [i] | ||
| 4 | Linear OOA(12827, 1786052, F128, 2, 9) (dual of [(1786052, 2), 3572077, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12827, 1786052, F128, 3, 9) (dual of [(1786052, 3), 5358129, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(12827, 1786052, F128, 4, 9) (dual of [(1786052, 4), 7144181, 10]-NRT-code) | [i] | ||
| 7 | Digital (18, 27, 1786052)-net over F128 | [i] | ||
| 8 | Linear OOA(12827, 1048581, F128, 2, 9) (dual of [(1048581, 2), 2097135, 10]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12827, 699054, F128, 3, 9) (dual of [(699054, 3), 2097135, 10]-NRT-code) | [i] | ||
| 10 | Linear OOA(12827, 524290, F128, 9, 9) (dual of [(524290, 9), 4718583, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |