Information on Result #684581
Linear OA(784, 823584, F7, 13) (dual of [823584, 823500, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(76, 41, F7, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-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(785, 823585, F7, 13) (dual of [823585, 823500, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(786, 823586, F7, 13) (dual of [823586, 823500, 14]-code) | [i] | ||
| 3 | Linear OA(787, 823587, F7, 13) (dual of [823587, 823500, 14]-code) | [i] | ||
| 4 | Linear OA(788, 823588, F7, 13) (dual of [823588, 823500, 14]-code) | [i] | ||
| 5 | Linear OOA(784, 823584, F7, 2, 13) (dual of [(823584, 2), 1647084, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(784, 823584, F7, 3, 13) (dual of [(823584, 3), 2470668, 14]-NRT-code) | [i] | ||
| 7 | Digital (71, 84, 823584)-net over F7 | [i] | ||
| 8 | Linear OOA(784, 411792, F7, 2, 13) (dual of [(411792, 2), 823500, 14]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(784, 274528, F7, 3, 13) (dual of [(274528, 3), 823500, 14]-NRT-code) | [i] | ||
| 10 | Linear OOA(784, 137263, F7, 13, 13) (dual of [(137263, 13), 1784335, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |