Information on Result #684503
Linear OA(758, 5764811, F7, 9) (dual of [5764811, 5764753, 10]-code), using construction X4 applied to C([0,8]) ⊂ C([1,7]) based on
- linear OA(757, 5764800, F7, 9) (dual of [5764800, 5764743, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(748, 5764800, F7, 7) (dual of [5764800, 5764752, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(710, 11, F7, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,7)), using
- dual of repetition code with length 11 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), 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(758, 4288245, F7, 2, 9) (dual of [(4288245, 2), 8576432, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(758, 4288245, F7, 3, 9) (dual of [(4288245, 3), 12864677, 10]-NRT-code) | [i] | ||
| 3 | Digital (49, 58, 4288245)-net over F7 | [i] | ||
| 4 | Linear OOA(758, 2882405, F7, 2, 9) (dual of [(2882405, 2), 5764752, 10]-NRT-code) | [i] | OOA Folding | |