Information on Result #699745
Linear OA(12857, 2097163, F128, 19) (dual of [2097163, 2097106, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(16100, 2097163, S16, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3280, 2097163, S32, 19) | [i] | ||
| 3 | OA(6467, 2097163, S64, 19) | [i] | ||
| 4 | Linear OOA(12857, 1048581, F128, 2, 19) (dual of [(1048581, 2), 2097105, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12857, 699054, F128, 3, 19) (dual of [(699054, 3), 2097105, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(12857, 233018, F128, 19, 19) (dual of [(233018, 19), 4427285, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |