Information on Result #731093
Linear OA(826, 524294, F8, 5) (dual of [524294, 524268, 6]-code), using trace code based on linear OA(6413, 262147, F64, 5) (dual of [262147, 262134, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-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(827, 524295, F8, 5) (dual of [524295, 524268, 6]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(826, 524294, F8, 2, 5) (dual of [(524294, 2), 1048562, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(826, 524294, F8, 3, 5) (dual of [(524294, 3), 1572856, 6]-NRT-code) | [i] | ||
| 4 | Digital (21, 26, 524294)-net over F8 | [i] | ||
| 5 | Linear OOA(826, 262147, F8, 2, 5) (dual of [(262147, 2), 524268, 6]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(826, 262146, F8, 3, 5) (dual of [(262146, 3), 786412, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 7 | Linear OOA(826, 262146, F8, 5, 5) (dual of [(262146, 5), 1310704, 6]-NRT-code) | [i] | ||