Information on Result #684600
Linear OA(751, 823552, F7, 9) (dual of [823552, 823501, 10]-code), using construction X4 applied to C([0,8]) ⊂ C([1,7]) based on
- linear OA(750, 823542, F7, 9) (dual of [823542, 823492, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(742, 823542, F7, 7) (dual of [823542, 823500, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(79, 10, F7, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,7)), using
- dual of repetition code with length 10 [i]
- linear OA(71, 10, F7, 1) (dual of [10, 9, 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(751, 612603, F7, 2, 9) (dual of [(612603, 2), 1225155, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(751, 612603, F7, 3, 9) (dual of [(612603, 3), 1837758, 10]-NRT-code) | [i] | ||
| 3 | Digital (42, 51, 612603)-net over F7 | [i] | ||
| 4 | Linear OOA(751, 411776, F7, 2, 9) (dual of [(411776, 2), 823501, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(751, 274517, F7, 3, 9) (dual of [(274517, 3), 823500, 10]-NRT-code) | [i] | ||