Information on Result #1464563
Linear OOA(12841, 1777424, F128, 2, 13) (dual of [(1777424, 2), 3554807, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12841, 1777424, F128, 13) (dual of [1777424, 1777383, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, 2097171, F128, 13) (dual of [2097171, 2097130, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- 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(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), using
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- Reed–Solomon code RS(124,128) [i]
- discarding factors / shortening the dual code based on linear OA(1284, 128, F128, 4) (dual of [128, 124, 5]-code or 128-arc in PG(3,128)), using
- construction X applied to Ce(12) ⊂ Ce(7) [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 | OOA(6448, 1777424, S64, 2, 13) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(12841, 888712, F128, 3, 13) (dual of [(888712, 3), 2666095, 14]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(12841, 888712, F128, 4, 13) (dual of [(888712, 4), 3554807, 14]-NRT-code) | [i] | ||