Information on Result #1310780
Linear OA(589, 678, F5, 27) (dual of [678, 589, 28]-code), using 45 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0) 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: 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(589, 678, F5, 2, 27) (dual of [(678, 2), 1267, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(589, 678, F5, 3, 27) (dual of [(678, 3), 1945, 28]-NRT-code) | [i] | ||
| 3 | Digital (62, 89, 678)-net over F5 | [i] | ||
| 4 | Linear OOA(589, 339, F5, 2, 27) (dual of [(339, 2), 589, 28]-NRT-code) | [i] | OOA Folding | |