Information on Result #677034
Linear OA(377, 747, F3, 18) (dual of [747, 670, 19]-code), using construction XX applied to Ce(18) ⊂ Ce(15) ⊂ 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(361, 729, F3, 16) (dual of [729, 668, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
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(377, 614, F3, 2, 18) (dual of [(614, 2), 1151, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(377, 614, F3, 3, 18) (dual of [(614, 3), 1765, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(377, 614, F3, 4, 18) (dual of [(614, 4), 2379, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(377, 614, F3, 5, 18) (dual of [(614, 5), 2993, 19]-NRT-code) | [i] | ||
| 5 | Digital (59, 77, 614)-net over F3 | [i] | ||