Information on Result #684882
Linear OA(7106, 2411, F7, 31) (dual of [2411, 2305, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,14]) based on
- linear OA(7105, 2402, F7, 31) (dual of [2402, 2297, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(797, 2402, F7, 29) (dual of [2402, 2305, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [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(7107, 2412, F7, 31) (dual of [2412, 2305, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(7108, 2413, F7, 31) (dual of [2413, 2305, 32]-code) | [i] | ||
| 3 | Linear OOA(7106, 2215, F7, 2, 31) (dual of [(2215, 2), 4324, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(7106, 2215, F7, 3, 31) (dual of [(2215, 3), 6539, 32]-NRT-code) | [i] | ||
| 5 | Digital (75, 106, 2215)-net over F7 | [i] | ||
| 6 | Linear OA(7108, 2414, F7, 31) (dual of [2414, 2306, 32]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(7106, 1205, F7, 2, 31) (dual of [(1205, 2), 2304, 32]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(7106, 803, F7, 3, 31) (dual of [(803, 3), 2303, 32]-NRT-code) | [i] | ||