Information on Result #675469
Linear OA(3162, 6578, F3, 30) (dual of [6578, 6416, 31]-code), using construction X applied to Ce(30) ⊂ Ce(27) based on
- linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 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(3163, 6579, F3, 30) (dual of [6579, 6416, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3162, 3289, F3, 2, 30) (dual of [(3289, 2), 6416, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3162, 2192, F3, 3, 30) (dual of [(2192, 3), 6414, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3162, 1644, F3, 4, 30) (dual of [(1644, 4), 6414, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(3162, 1315, F3, 5, 30) (dual of [(1315, 5), 6413, 31]-NRT-code) | [i] | ||