Information on Result #682356
Linear OA(5119, 390656, F5, 18) (dual of [390656, 390537, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(13) ⊂ Ce(12) based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(581, 390625, F5, 13) (dual of [390625, 390544, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(55, 30, F5, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(5119, 242864, F5, 2, 18) (dual of [(242864, 2), 485609, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5119, 242864, F5, 3, 18) (dual of [(242864, 3), 728473, 19]-NRT-code) | [i] | ||
| 3 | Digital (101, 119, 242864)-net over F5 | [i] | ||
| 4 | Linear OOA(5119, 195328, F5, 2, 18) (dual of [(195328, 2), 390537, 19]-NRT-code) | [i] | OOA Folding | |