Information on Result #698375
Linear OA(6426, 262152, F64, 9) (dual of [262152, 262126, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,3]) based on
- linear OA(6425, 262145, F64, 9) (dual of [262145, 262120, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(6419, 262145, F64, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 | OA(1639, 262152, S16, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3232, 262152, S32, 9) | [i] | ||
| 3 | Linear OOA(6426, 151431, F64, 2, 9) (dual of [(151431, 2), 302836, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6426, 151431, F64, 3, 9) (dual of [(151431, 3), 454267, 10]-NRT-code) | [i] | ||
| 5 | Digital (17, 26, 151431)-net over F64 | [i] | ||
| 6 | Linear OOA(6426, 131076, F64, 2, 9) (dual of [(131076, 2), 262126, 10]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6426, 87384, F64, 3, 9) (dual of [(87384, 3), 262126, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(6426, 65537, F64, 9, 9) (dual of [(65537, 9), 589807, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |