Information on Result #2277543
Linear OA(584, 628, F5, 27) (dual of [628, 544, 28]-code), using 1 times code embedding in larger space based on linear OA(583, 627, F5, 27) (dual of [627, 544, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(583, 625, F5, 27) (dual of [625, 542, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(581, 625, F5, 26) (dual of [625, 544, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-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(584, 516, F5, 2, 27) (dual of [(516, 2), 948, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(584, 516, F5, 3, 27) (dual of [(516, 3), 1464, 28]-NRT-code) | [i] | ||
| 3 | Digital (57, 84, 516)-net over F5 | [i] | ||
| 4 | Linear OOA(584, 314, F5, 2, 27) (dual of [(314, 2), 544, 28]-NRT-code) | [i] | OOA Folding | |