Information on Result #698468
Linear OA(6423, 262151, F64, 8) (dual of [262151, 262128, 9]-code), using construction X applied to Ce(7) ⊂ Ce(5) based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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 | Linear OA(846, 524302, F8, 8) (dual of [524302, 524256, 9]-code) | [i] | Trace Code | |
| 2 | OA(1635, 262151, S16, 8) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(3228, 262151, S32, 8) | [i] | ||
| 4 | Linear OOA(6423, 199314, F64, 2, 8) (dual of [(199314, 2), 398605, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(6423, 199314, F64, 3, 8) (dual of [(199314, 3), 597919, 9]-NRT-code) | [i] | ||
| 6 | Digital (15, 23, 199314)-net over F64 | [i] | ||
| 7 | Linear OOA(6423, 131075, F64, 2, 8) (dual of [(131075, 2), 262127, 9]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(6423, 87383, F64, 3, 8) (dual of [(87383, 3), 262126, 9]-NRT-code) | [i] | ||
| 9 | Linear OOA(6423, 65537, F64, 8, 8) (dual of [(65537, 8), 524273, 9]-NRT-code) | [i] | OA Folding and Stacking | |