Information on Result #684891
Linear OA(774, 2411, F7, 21) (dual of [2411, 2337, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(773, 2402, F7, 21) (dual of [2402, 2329, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(765, 2402, F7, 19) (dual of [2402, 2337, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(775, 2412, F7, 21) (dual of [2412, 2337, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(774, 2322, F7, 2, 21) (dual of [(2322, 2), 4570, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(774, 2322, F7, 3, 21) (dual of [(2322, 3), 6892, 22]-NRT-code) | [i] | ||
| 4 | Digital (53, 74, 2322)-net over F7 | [i] | ||
| 5 | Linear OA(775, 2413, F7, 21) (dual of [2413, 2338, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(774, 1205, F7, 2, 21) (dual of [(1205, 2), 2336, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(774, 803, F7, 3, 21) (dual of [(803, 3), 2335, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(774, 241, F7, 21, 21) (dual of [(241, 21), 4987, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |