Information on Result #684893
Linear OA(758, 2411, F7, 17) (dual of [2411, 2353, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(757, 2402, F7, 17) (dual of [2402, 2345, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(749, 2402, F7, 15) (dual of [2402, 2353, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(759, 2412, F7, 17) (dual of [2412, 2353, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(760, 2413, F7, 17) (dual of [2413, 2353, 18]-code) | [i] | ||
| 3 | Linear OOA(758, 1733, F7, 2, 17) (dual of [(1733, 2), 3408, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(758, 1733, F7, 3, 17) (dual of [(1733, 3), 5141, 18]-NRT-code) | [i] | ||
| 5 | Digital (41, 58, 1733)-net over F7 | [i] | ||
| 6 | Linear OA(760, 2418, F7, 17) (dual of [2418, 2358, 18]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(760, 2414, F7, 17) (dual of [2414, 2354, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(758, 1205, F7, 2, 17) (dual of [(1205, 2), 2352, 18]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(758, 803, F7, 3, 17) (dual of [(803, 3), 2351, 18]-NRT-code) | [i] | ||
| 10 | Linear OOA(758, 301, F7, 17, 17) (dual of [(301, 17), 5059, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |