Information on Result #953170
Linear OOA(3177, 177160, F3, 3, 22) (dual of [(177160, 3), 531303, 23]-NRT-code), using OOA 3-folding based on linear OA(3177, 531480, F3, 22) (dual of [531480, 531303, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3177, 531482, F3, 22) (dual of [531482, 531305, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(21) ⊂ Ce(16) [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(3177, 154605, F3, 4, 22) (dual of [(154605, 4), 618243, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3177, 154605, F3, 5, 22) (dual of [(154605, 5), 772848, 23]-NRT-code) | [i] | ||
| 3 | Digital (155, 177, 154605)-net over F3 | [i] | ||