Information on Result #699685
Linear OA(12856, 2097184, F128, 17) (dual of [2097184, 2097128, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,4]) based on
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), 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 | Linear OOA(12856, 2097184, F128, 2, 17) (dual of [(2097184, 2), 4194312, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12856, 2097184, F128, 3, 17) (dual of [(2097184, 3), 6291496, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(12856, 2097184, F128, 4, 17) (dual of [(2097184, 4), 8388680, 18]-NRT-code) | [i] | ||
| 4 | Digital (39, 56, 2097184)-net over F128 | [i] | ||
| 5 | Linear OOA(12856, 1048592, F128, 2, 17) (dual of [(1048592, 2), 2097128, 18]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12856, 699061, F128, 3, 17) (dual of [(699061, 3), 2097127, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(12856, 524296, F128, 4, 17) (dual of [(524296, 4), 2097128, 18]-NRT-code) | [i] | ||