Information on Result #731149
Linear OA(882, 524302, F8, 14) (dual of [524302, 524220, 15]-code), using trace code based on linear OA(6441, 262151, F64, 14) (dual of [262151, 262110, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(883, 524303, F8, 14) (dual of [524303, 524220, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(882, 524302, F8, 2, 14) (dual of [(524302, 2), 1048522, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(882, 524302, F8, 3, 14) (dual of [(524302, 3), 1572824, 15]-NRT-code) | [i] | ||
| 4 | Digital (68, 82, 524302)-net over F8 | [i] | ||
| 5 | Linear OA(883, 524304, F8, 14) (dual of [524304, 524221, 15]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(882, 262151, F8, 2, 14) (dual of [(262151, 2), 524220, 15]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(882, 174767, F8, 3, 14) (dual of [(174767, 3), 524219, 15]-NRT-code) | [i] | ||
| 8 | Linear OOA(882, 74900, F8, 14, 14) (dual of [(74900, 14), 1048518, 15]-NRT-code) | [i] | OA Folding and Stacking | |