Information on Result #691896
Linear OA(1646, 4112, F16, 15) (dual of [4112, 4066, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,5]) based on
- linear OA(1643, 4097, F16, 15) (dual of [4097, 4054, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(1631, 4097, F16, 11) (dual of [4097, 4066, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(1647, 4113, F16, 15) (dual of [4113, 4066, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1646, 2056, F16, 2, 15) (dual of [(2056, 2), 4066, 16]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(1646, 587, F16, 15, 15) (dual of [(587, 15), 8759, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |