Information on Result #1567102
Linear OOA(12873, 910041, F128, 3, 24) (dual of [(910041, 3), 2730050, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12873, 910041, F128, 2, 24) (dual of [(910041, 2), 1820009, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12873, 1048583, F128, 2, 24) (dual of [(1048583, 2), 2097093, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12873, 2097166, F128, 24) (dual of [2097166, 2097093, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12873, 2097167, F128, 24) (dual of [2097167, 2097094, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12873, 2097167, F128, 24) (dual of [2097167, 2097094, 25]-code), using
- OOA 2-folding [i] based on linear OA(12873, 2097166, F128, 24) (dual of [2097166, 2097093, 25]-code), using
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 | OOA(6486, 910041, S64, 3, 24) | [i] | Discarding Parts of the Base for OOAs | |