Information on Result #675287
Linear OA(378, 19709, F3, 12) (dual of [19709, 19631, 13]-code), using construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(7) based on
- linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(355, 19683, F3, 10) (dual of [19683, 19628, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(346, 19683, F3, 8) (dual of [19683, 19637, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(31, 22, F3, 1) (dual of [22, 21, 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, 4, F3, 1) (dual of [4, 3, 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 (see above)
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(378, 10676, F3, 2, 12) (dual of [(10676, 2), 21274, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(378, 10676, F3, 3, 12) (dual of [(10676, 3), 31950, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(378, 10676, F3, 4, 12) (dual of [(10676, 4), 42626, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(378, 10676, F3, 5, 12) (dual of [(10676, 5), 53302, 13]-NRT-code) | [i] | ||
| 5 | Digital (66, 78, 10676)-net over F3 | [i] | ||
| 6 | Linear OOA(378, 9854, F3, 2, 12) (dual of [(9854, 2), 19630, 13]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(378, 4927, F3, 4, 12) (dual of [(4927, 4), 19630, 13]-NRT-code) | [i] | ||