Information on Result #692560
Linear OA(1672, 268, F16, 39) (dual of [268, 196, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,17]) based on
- linear OA(1669, 257, F16, 39) (dual of [257, 188, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(1661, 257, F16, 35) (dual of [257, 196, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 257 | 164−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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 OA(1673, 269, F16, 39) (dual of [269, 196, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1674, 270, F16, 39) (dual of [270, 196, 40]-code) | [i] | ||
| 3 | Linear OA(1671, 267, F16, 38) (dual of [267, 196, 39]-code) | [i] | Truncation | |
| 4 | Linear OA(1675, 274, F16, 39) (dual of [274, 199, 40]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(1672, 134, F16, 2, 39) (dual of [(134, 2), 196, 40]-NRT-code) | [i] | OOA Folding | |