Information on Result #1464852
Linear OOA(12864, 1411103, F128, 2, 20) (dual of [(1411103, 2), 2822142, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12864, 1411103, F128, 20) (dual of [1411103, 1411039, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 2097179, F128, 20) (dual of [2097179, 2097115, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1286, 27, F128, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
Mode: 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(12864, 705551, F128, 3, 20) (dual of [(705551, 3), 2116589, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12864, 705551, F128, 4, 20) (dual of [(705551, 4), 2822140, 21]-NRT-code) | [i] | ||