Information on Result #683263
Linear OA(542, 635, F5, 13) (dual of [635, 593, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(541, 626, F5, 13) (dual of [626, 585, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(533, 626, F5, 11) (dual of [626, 593, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 58−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(542, 488, F5, 2, 13) (dual of [(488, 2), 934, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(542, 488, F5, 3, 13) (dual of [(488, 3), 1422, 14]-NRT-code) | [i] | ||
| 3 | Digital (29, 42, 488)-net over F5 | [i] | ||
| 4 | Linear OOA(542, 317, F5, 2, 13) (dual of [(317, 2), 592, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(542, 211, F5, 3, 13) (dual of [(211, 3), 591, 14]-NRT-code) | [i] | ||