Information on Result #683255
Linear OA(574, 635, F5, 23) (dual of [635, 561, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(573, 626, F5, 23) (dual of [626, 553, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(565, 626, F5, 21) (dual of [626, 561, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(574, 570, F5, 2, 23) (dual of [(570, 2), 1066, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(574, 570, F5, 3, 23) (dual of [(570, 3), 1636, 24]-NRT-code) | [i] | ||
| 3 | Digital (51, 74, 570)-net over F5 | [i] | ||
| 4 | Linear OOA(574, 317, F5, 2, 23) (dual of [(317, 2), 560, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(574, 211, F5, 3, 23) (dual of [(211, 3), 559, 24]-NRT-code) | [i] | ||