Information on Result #682863
Linear OA(532, 15633, F5, 7) (dual of [15633, 15601, 8]-code), using construction X4 applied to C([0,6]) ⊂ C([1,5]) based on
- linear OA(531, 15624, F5, 7) (dual of [15624, 15593, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(524, 15624, F5, 5) (dual of [15624, 15600, 6]-code), using the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(58, 9, F5, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,5)), using
- dual of repetition code with length 9 [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(532, 14038, F5, 2, 7) (dual of [(14038, 2), 28044, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(532, 14038, F5, 3, 7) (dual of [(14038, 3), 42082, 8]-NRT-code) | [i] | ||
| 3 | Digital (25, 32, 14038)-net over F5 | [i] | ||
| 4 | Linear OA(533, 15635, F5, 7) (dual of [15635, 15602, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(532, 7816, F5, 2, 7) (dual of [(7816, 2), 15600, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(532, 5211, F5, 3, 7) (dual of [(5211, 3), 15601, 8]-NRT-code) | [i] | ||