Information on Result #699746
Linear OA(12854, 2097163, F128, 18) (dual of [2097163, 2097109, 19]-code), using construction X applied to Ce(17) ⊂ Ce(14) 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(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(1695, 2097163, S16, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3276, 2097163, S32, 18) | [i] | ||
| 3 | OA(6463, 2097163, S64, 18) | [i] | ||
| 4 | Linear OOA(12854, 1048581, F128, 2, 18) (dual of [(1048581, 2), 2097108, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12854, 699054, F128, 3, 18) (dual of [(699054, 3), 2097108, 19]-NRT-code) | [i] | ||
| 6 | Linear OOA(12854, 524290, F128, 4, 18) (dual of [(524290, 4), 2097106, 19]-NRT-code) | [i] | ||
| 7 | Linear OOA(12854, 233018, F128, 18, 18) (dual of [(233018, 18), 4194270, 19]-NRT-code) | [i] | OA Folding and Stacking | |