Information on Result #684984
Linear OA(734, 2410, F7, 10) (dual of [2410, 2376, 11]-code), using construction X applied to Ce(9) ⊂ Ce(7) based on
- linear OA(733, 2401, F7, 10) (dual of [2401, 2368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(725, 2401, F7, 8) (dual of [2401, 2376, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(735, 2411, F7, 10) (dual of [2411, 2376, 11]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(734, 1917, F7, 2, 10) (dual of [(1917, 2), 3800, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(734, 1917, F7, 3, 10) (dual of [(1917, 3), 5717, 11]-NRT-code) | [i] | ||
| 4 | Digital (24, 34, 1917)-net over F7 | [i] | ||
| 5 | Linear OA(735, 2412, F7, 10) (dual of [2412, 2377, 11]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(736, 2414, F7, 10) (dual of [2414, 2378, 11]-code) | [i] | ||
| 7 | Linear OOA(734, 1205, F7, 2, 10) (dual of [(1205, 2), 2376, 11]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(734, 803, F7, 3, 10) (dual of [(803, 3), 2375, 11]-NRT-code) | [i] | ||
| 9 | Linear OOA(734, 482, F7, 10, 10) (dual of [(482, 10), 4786, 11]-NRT-code) | [i] | OA Folding and Stacking | |