Information on Result #684709
Linear OA(7102, 16819, F7, 23) (dual of [16819, 16717, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(7101, 16808, F7, 23) (dual of [16808, 16707, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(791, 16808, F7, 21) (dual of [16808, 16717, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 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 OOA(7102, 16770, F7, 2, 23) (dual of [(16770, 2), 33438, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7102, 16770, F7, 3, 23) (dual of [(16770, 3), 50208, 24]-NRT-code) | [i] | ||
| 3 | Digital (79, 102, 16770)-net over F7 | [i] | ||