Information on Result #699863
Linear OA(12830, 16402, F128, 13) (dual of [16402, 16372, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,3]) based on
- linear OA(12825, 16385, F128, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(12813, 16385, F128, 7) (dual of [16385, 16372, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [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(6435, 16402, S64, 13) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12830, 13882, F128, 2, 13) (dual of [(13882, 2), 27734, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12830, 13882, F128, 3, 13) (dual of [(13882, 3), 41616, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(12830, 13882, F128, 4, 13) (dual of [(13882, 4), 55498, 14]-NRT-code) | [i] | ||
| 5 | Digital (17, 30, 13882)-net over F128 | [i] | ||
| 6 | Linear OOA(12830, 8201, F128, 2, 13) (dual of [(8201, 2), 16372, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12830, 5467, F128, 3, 13) (dual of [(5467, 3), 16371, 14]-NRT-code) | [i] | ||
| 8 | Linear OOA(12830, 4100, F128, 4, 13) (dual of [(4100, 4), 16370, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(12830, 2733, F128, 13, 13) (dual of [(2733, 13), 35499, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |