Information on Result #953275
Linear OOA(3172, 59062, F3, 3, 23) (dual of [(59062, 3), 177014, 24]-NRT-code), using OOA 3-folding based on linear OA(3172, 177186, F3, 23) (dual of [177186, 177014, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3133, 177147, F3, 19) (dual of [177147, 177014, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3175, 59063, F3, 3, 23) (dual of [(59063, 3), 177014, 24]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3173, 59062, F3, 3, 23) (dual of [(59062, 3), 177013, 24]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3174, 59062, F3, 3, 23) (dual of [(59062, 3), 177012, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(3172, 59062, F3, 4, 23) (dual of [(59062, 4), 236076, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3172, 59062, F3, 5, 23) (dual of [(59062, 5), 295138, 24]-NRT-code) | [i] | ||
| 6 | Digital (149, 172, 59062)-net over F3 | [i] | ||