Information on Result #676686
Linear OA(3104, 754, F3, 25) (dual of [754, 650, 26]-code), using construction X applied to Ce(24) ⊂ Ce(19) based on
- linear OA(397, 729, F3, 25) (dual of [729, 632, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(379, 729, F3, 20) (dual of [729, 650, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(3104, 626, F3, 2, 25) (dual of [(626, 2), 1148, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3104, 626, F3, 3, 25) (dual of [(626, 3), 1774, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(3104, 626, F3, 4, 25) (dual of [(626, 4), 2400, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(3104, 626, F3, 5, 25) (dual of [(626, 5), 3026, 26]-NRT-code) | [i] | ||
| 5 | Digital (79, 104, 626)-net over F3 | [i] | ||