Information on Result #2279124
Linear OA(7101, 823560, F7, 17) (dual of [823560, 823459, 18]-code), using 1 times code embedding in larger space based on linear OA(7100, 823559, F7, 17) (dual of [823559, 823459, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(799, 823544, F7, 17) (dual of [823544, 823445, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 823544 | 714−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(785, 823544, F7, 15) (dual of [823544, 823459, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 823544 | 714−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(71, 15, F7, 1) (dual of [15, 14, 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(7101, 460886, F7, 2, 17) (dual of [(460886, 2), 921671, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7101, 460886, F7, 3, 17) (dual of [(460886, 3), 1382557, 18]-NRT-code) | [i] | ||
| 3 | Digital (84, 101, 460886)-net over F7 | [i] | ||
| 4 | Linear OOA(7101, 411780, F7, 2, 17) (dual of [(411780, 2), 823459, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7101, 274520, F7, 3, 17) (dual of [(274520, 3), 823459, 18]-NRT-code) | [i] | ||