Information on Result #2248367
Linear OA(743, 823551, F7, 7) (dual of [823551, 823508, 8]-code), using 1 times truncation based on linear OA(744, 823552, F7, 8) (dual of [823552, 823508, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of 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(736, 823543, F7, 6) (dual of [823543, 823507, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(78, 9, F7, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,7)), using
- dual of repetition code with length 9 [i]
- linear OA(71, 9, F7, 1) (dual of [9, 8, 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(743, 823551, F7, 2, 7) (dual of [(823551, 2), 1647059, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(743, 823551, F7, 3, 7) (dual of [(823551, 3), 2470610, 8]-NRT-code) | [i] | ||
| 3 | Digital (36, 43, 823551)-net over F7 | [i] | ||
| 4 | Linear OOA(743, 411775, F7, 2, 7) (dual of [(411775, 2), 823507, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(743, 274517, F7, 3, 7) (dual of [(274517, 3), 823508, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(743, 274516, F7, 7, 7) (dual of [(274516, 7), 1921569, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |