Information on Result #1304925
Linear OA(3158, 819, F3, 38) (dual of [819, 661, 39]-code), using 74 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 12 times 0, 1, 16 times 0, 1, 19 times 0) based on linear OA(3148, 735, F3, 38) (dual of [735, 587, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- linear OA(3148, 729, F3, 38) (dual of [729, 581, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3142, 729, F3, 37) (dual of [729, 587, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(3158, 819, F3, 2, 38) (dual of [(819, 2), 1480, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3158, 819, F3, 3, 38) (dual of [(819, 3), 2299, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(3158, 819, F3, 4, 38) (dual of [(819, 4), 3118, 39]-NRT-code) | [i] | ||
| 4 | Linear OOA(3158, 819, F3, 5, 38) (dual of [(819, 5), 3937, 39]-NRT-code) | [i] | ||
| 5 | Digital (120, 158, 819)-net over F3 | [i] | ||
| 6 | Linear OOA(3158, 409, F3, 2, 38) (dual of [(409, 2), 660, 39]-NRT-code) | [i] | OOA Folding | |