Information on Result #1566431
Linear OOA(12827, 6606, F128, 3, 13) (dual of [(6606, 3), 19791, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12827, 6606, F128, 2, 13) (dual of [(6606, 2), 13185, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12827, 8196, F128, 2, 13) (dual of [(8196, 2), 16365, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12827, 16392, F128, 13) (dual of [16392, 16365, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(12827, 16392, F128, 13) (dual of [16392, 16365, 14]-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(6432, 6606, S64, 3, 13) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(12827, 3302, F128, 15, 13) (dual of [(3302, 15), 49503, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |