Information on Result #2245767
Linear OA(533, 390634, F5, 5) (dual of [390634, 390601, 6]-code), using 1 times truncation based on linear OA(534, 390635, F5, 6) (dual of [390635, 390601, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(525, 390625, F5, 4) (dual of [390625, 390600, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(59, 10, F5, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,5)), using
- dual of repetition code with length 10 [i]
- linear OA(51, 10, F5, 1) (dual of [10, 9, 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(533, 390634, F5, 2, 5) (dual of [(390634, 2), 781235, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(533, 390634, F5, 3, 5) (dual of [(390634, 3), 1171869, 6]-NRT-code) | [i] | ||
| 3 | Digital (28, 33, 390634)-net over F5 | [i] | ||
| 4 | Linear OOA(533, 195317, F5, 2, 5) (dual of [(195317, 2), 390601, 6]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(533, 195316, F5, 3, 5) (dual of [(195316, 3), 585915, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 6 | Linear OOA(533, 195316, F5, 5, 5) (dual of [(195316, 5), 976547, 6]-NRT-code) | [i] | ||