Information on Result #684555
Linear OA(737, 823559, F7, 6) (dual of [823559, 823522, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- 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(722, 823543, F7, 4) (dual of [823543, 823521, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 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 OA(738, 823560, F7, 6) (dual of [823560, 823522, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(737, 823559, F7, 2, 6) (dual of [(823559, 2), 1647081, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(737, 823559, F7, 3, 6) (dual of [(823559, 3), 2470640, 7]-NRT-code) | [i] | ||
| 4 | Digital (31, 37, 823559)-net over F7 | [i] | ||