Information on Result #685157
Linear OA(744, 351, F7, 17) (dual of [351, 307, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(743, 344, F7, 17) (dual of [344, 301, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 344 | 76−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(737, 344, F7, 15) (dual of [344, 307, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 344 | 76−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 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(744, 275, F7, 2, 17) (dual of [(275, 2), 506, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(744, 275, F7, 3, 17) (dual of [(275, 3), 781, 18]-NRT-code) | [i] | ||
| 3 | Digital (27, 44, 275)-net over F7 | [i] | ||
| 4 | Linear OOA(744, 175, F7, 2, 17) (dual of [(175, 2), 306, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(744, 117, F7, 3, 17) (dual of [(117, 3), 307, 18]-NRT-code) | [i] | ||