Information on Result #1304377
Linear OA(3112, 772, F3, 26) (dual of [772, 660, 27]-code), using 28 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0) based on linear OA(3103, 735, F3, 26) (dual of [735, 632, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3103, 729, F3, 26) (dual of [729, 626, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(397, 729, F3, 25) (dual of [729, 632, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 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(3112, 767, F3, 2, 26) (dual of [(767, 2), 1422, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3112, 767, F3, 3, 26) (dual of [(767, 3), 2189, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3112, 767, F3, 4, 26) (dual of [(767, 4), 2956, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(3112, 767, F3, 5, 26) (dual of [(767, 5), 3723, 27]-NRT-code) | [i] | ||
| 5 | Digital (86, 112, 767)-net over F3 | [i] | ||