Information on Result #698380
Linear OA(6414, 262153, F64, 5) (dual of [262153, 262139, 6]-code), using construction X4 applied to C([0,2]) ⊂ C([0,1]) based on
- linear OA(6413, 262145, F64, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(647, 262145, F64, 3) (dual of [262145, 262138, 4]-code or 262145-cap in PG(6,64)), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(647, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), 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(828, 524306, F8, 5) (dual of [524306, 524278, 6]-code) | [i] | Trace Code | |
| 2 | Linear OOA(6414, 262153, F64, 2, 5) (dual of [(262153, 2), 524292, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6414, 262153, F64, 3, 5) (dual of [(262153, 3), 786445, 6]-NRT-code) | [i] | ||
| 4 | Digital (9, 14, 262153)-net over F64 | [i] | ||
| 5 | Linear OOA(6414, 131076, F64, 3, 5) (dual of [(131076, 3), 393214, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 6 | Linear OOA(6414, 131076, F64, 5, 5) (dual of [(131076, 5), 655366, 6]-NRT-code) | [i] | ||