Information on Result #691885
Linear OA(16112, 4112, F16, 39) (dual of [4112, 4000, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,17]) based on
- linear OA(16109, 4097, F16, 39) (dual of [4097, 3988, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(1697, 4097, F16, 35) (dual of [4097, 4000, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(163, 15, F16, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,16) or 15-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(16113, 4113, F16, 39) (dual of [4113, 4000, 40]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16112, 3982, F16, 2, 39) (dual of [(3982, 2), 7852, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (73, 112, 3982)-net over F16 | [i] | ||
| 4 | Linear OA(16113, 4114, F16, 39) (dual of [4114, 4001, 40]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(16112, 2056, F16, 2, 39) (dual of [(2056, 2), 4000, 40]-NRT-code) | [i] | OOA Folding | |