Information on Result #2661689
Linear OOA(3249, 177161, F3, 3, 30) (dual of [(177161, 3), 531234, 31]-NRT-code), using 1 step truncation based on linear OOA(3250, 177162, F3, 3, 31) (dual of [(177162, 3), 531236, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3250, 531486, F3, 31) (dual of [531486, 531236, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3241, 531441, F3, 31) (dual of [531441, 531200, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3205, 531441, F3, 26) (dual of [531441, 531236, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
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(3249, 172386, F3, 4, 30) (dual of [(172386, 4), 689295, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3249, 172386, F3, 5, 30) (dual of [(172386, 5), 861681, 31]-NRT-code) | [i] | ||
| 3 | Digital (219, 249, 172386)-net over F3 | [i] | ||