Information on Result #1310786
Linear OA(5112, 3170, F5, 27) (dual of [3170, 3058, 28]-code), using 34 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 0, 0, 0, 1, 8 times 0, 1, 18 times 0) based on linear OA(5106, 3130, F5, 27) (dual of [3130, 3024, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(5106, 3125, F5, 27) (dual of [3125, 3019, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(5101, 3125, F5, 26) (dual of [3125, 3024, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 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(5112, 3170, F5, 2, 27) (dual of [(3170, 2), 6228, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5112, 3170, F5, 3, 27) (dual of [(3170, 3), 9398, 28]-NRT-code) | [i] | ||
| 3 | Digital (85, 112, 3170)-net over F5 | [i] | ||
| 4 | Linear OOA(5112, 1585, F5, 2, 27) (dual of [(1585, 2), 3058, 28]-NRT-code) | [i] | OOA Folding | |