Information on Result #700050
Linear OA(12828, 16401, F128, 12) (dual of [16401, 16373, 13]-code), using construction X applied to Ce(11) ⊂ Ce(5) based on
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), 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 | OA(6433, 16401, S64, 12) | [i] | Discarding Parts of the Base for OAs | |
2 | Linear OOA(12828, 16401, F128, 2, 12) (dual of [(16401, 2), 32774, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
3 | Linear OOA(12828, 16401, F128, 3, 12) (dual of [(16401, 3), 49175, 13]-NRT-code) | [i] | ||
4 | Linear OOA(12828, 16401, F128, 4, 12) (dual of [(16401, 4), 65576, 13]-NRT-code) | [i] | ||
5 | Digital (16, 28, 16401)-net over F128 | [i] | ||
6 | Linear OOA(12828, 8200, F128, 2, 12) (dual of [(8200, 2), 16372, 13]-NRT-code) | [i] | OOA Folding | |
7 | Linear OOA(12828, 5467, F128, 3, 12) (dual of [(5467, 3), 16373, 13]-NRT-code) | [i] | ||
8 | Linear OOA(12828, 4100, F128, 4, 12) (dual of [(4100, 4), 16372, 13]-NRT-code) | [i] |