Information on Result #699813
Linear OA(12863, 2097187, F128, 19) (dual of [2097187, 2097124, 20]-code), using construction X applied to Ce(18) ⊂ Ce(9) 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(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(1288, 35, F128, 8) (dual of [35, 27, 9]-code or 35-arc in PG(7,128)), using
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- Reed–Solomon code RS(120,128) [i]
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), 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 | Linear OOA(12863, 2097187, F128, 2, 19) (dual of [(2097187, 2), 4194311, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12863, 2097187, F128, 3, 19) (dual of [(2097187, 3), 6291498, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(12863, 2097187, F128, 4, 19) (dual of [(2097187, 4), 8388685, 20]-NRT-code) | [i] | ||
| 4 | Digital (44, 63, 2097187)-net over F128 | [i] | ||
| 5 | Linear OOA(12863, 1048593, F128, 2, 19) (dual of [(1048593, 2), 2097123, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12863, 699062, F128, 3, 19) (dual of [(699062, 3), 2097123, 20]-NRT-code) | [i] | ||