Information on Result #683485
Linear OA(578, 634, F5, 24) (dual of [634, 556, 25]-code), using construction X applied to Ce(23) ⊂ Ce(21) based on
- linear OA(577, 625, F5, 24) (dual of [625, 548, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(569, 625, F5, 22) (dual of [625, 556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(578, 618, F5, 2, 24) (dual of [(618, 2), 1158, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 618, F5, 3, 24) (dual of [(618, 3), 1776, 25]-NRT-code) | [i] | ||
| 3 | Digital (54, 78, 618)-net over F5 | [i] | ||