Information on Result #684565
Linear OA(767, 823567, F7, 11) (dual of [823567, 823500, 12]-code), using construction X applied to Ce(10) ⊂ Ce(7) based on
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(73, 24, F7, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-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(768, 823568, F7, 11) (dual of [823568, 823500, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(767, 823567, F7, 2, 11) (dual of [(823567, 2), 1647067, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(767, 823567, F7, 3, 11) (dual of [(823567, 3), 2470634, 12]-NRT-code) | [i] | ||
| 4 | Digital (56, 67, 823567)-net over F7 | [i] | ||
| 5 | Linear OA(768, 823569, F7, 11) (dual of [823569, 823501, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(769, 823571, F7, 11) (dual of [823571, 823502, 12]-code) | [i] | ||
| 7 | Linear OOA(767, 411783, F7, 2, 11) (dual of [(411783, 2), 823499, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(767, 274522, F7, 3, 11) (dual of [(274522, 3), 823499, 12]-NRT-code) | [i] | ||
| 9 | Linear OOA(767, 164713, F7, 11, 11) (dual of [(164713, 11), 1811776, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |