Information on Result #699981
Linear OA(12837, 16392, F128, 18) (dual of [16392, 16355, 19]-code), using construction X applied to Ce(17) ⊂ Ce(14) based on
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-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(6444, 16392, S64, 18) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12837, 8196, F128, 2, 18) (dual of [(8196, 2), 16355, 19]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(12837, 5464, F128, 3, 18) (dual of [(5464, 3), 16355, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(12837, 4098, F128, 4, 18) (dual of [(4098, 4), 16355, 19]-NRT-code) | [i] | ||