Information on Result #692556
Linear OA(1688, 268, F16, 47) (dual of [268, 180, 48]-code), using construction X applied to C([0,23]) ⊂ C([0,21]) based on
- linear OA(1685, 257, F16, 47) (dual of [257, 172, 48]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,23], and minimum distance d ≥ |{−23,−22,…,23}|+1 = 48 (BCH-bound) [i]
- linear OA(1677, 257, F16, 43) (dual of [257, 180, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(163, 11, F16, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,16) or 11-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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(1688, 134, F16, 2, 47) (dual of [(134, 2), 180, 48]-NRT-code) | [i] | OOA Folding | |