Information on Result #686245
Linear OA(851, 2097160, F8, 9) (dual of [2097160, 2097109, 10]-code), using construction X applied to Ce(8) ⊂ Ce(6) based on
- linear OA(850, 2097152, F8, 9) (dual of [2097152, 2097102, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(843, 2097152, F8, 7) (dual of [2097152, 2097109, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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 OOA(851, 1362895, F8, 2, 9) (dual of [(1362895, 2), 2725739, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(851, 1362895, F8, 3, 9) (dual of [(1362895, 3), 4088634, 10]-NRT-code) | [i] | ||
| 3 | Digital (42, 51, 1362895)-net over F8 | [i] | ||
| 4 | Linear OOA(851, 1048580, F8, 2, 9) (dual of [(1048580, 2), 2097109, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(851, 699053, F8, 3, 9) (dual of [(699053, 3), 2097108, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(851, 524289, F8, 9, 9) (dual of [(524289, 9), 4718550, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |