Information on Result #692559
Linear OA(1676, 268, F16, 41) (dual of [268, 192, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,18]) based on
- linear OA(1673, 257, F16, 41) (dual of [257, 184, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(1665, 257, F16, 37) (dual of [257, 192, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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(1676, 134, F16, 2, 41) (dual of [(134, 2), 192, 42]-NRT-code) | [i] | OOA Folding | |