Information on Result #676694
Linear OA(380, 754, F3, 19) (dual of [754, 674, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
- linear OA(373, 729, F3, 19) (dual of [729, 656, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(355, 729, F3, 14) (dual of [729, 674, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), 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(380, 577, F3, 2, 19) (dual of [(577, 2), 1074, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(380, 577, F3, 3, 19) (dual of [(577, 3), 1651, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(380, 577, F3, 4, 19) (dual of [(577, 4), 2228, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(380, 577, F3, 5, 19) (dual of [(577, 5), 2805, 20]-NRT-code) | [i] | ||
| 5 | Digital (61, 80, 577)-net over F3 | [i] | ||