Information on Result #674419
Linear OA(354, 1594351, F3, 6) (dual of [1594351, 1594297, 7]-code), using construction X4 applied to Ce(6) ⊂ Ce(3) based on
- linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(327, 1594323, F3, 4) (dual of [1594323, 1594296, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
- dual of repetition code with length 28 [i]
- linear OA(31, 28, F3, 1) (dual of [28, 27, 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
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 OA(355, 1594352, F3, 6) (dual of [1594352, 1594297, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(354, 1594351, F3, 2, 6) (dual of [(1594351, 2), 3188648, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(354, 1594351, F3, 3, 6) (dual of [(1594351, 3), 4782999, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(354, 1594351, F3, 4, 6) (dual of [(1594351, 4), 6377350, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(354, 1594351, F3, 5, 6) (dual of [(1594351, 5), 7971701, 7]-NRT-code) | [i] | ||
| 6 | Linear OA(355, 1594353, F3, 6) (dual of [1594353, 1594298, 7]-code) | [i] | Construction X with Varšamov Bound | |