Information on Result #952744
Linear OOA(3147, 177156, F3, 3, 18) (dual of [(177156, 3), 531321, 19]-NRT-code), using OOA 3-folding based on linear OA(3147, 531468, F3, 18) (dual of [531468, 531321, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3146, 531467, F3, 18) (dual of [531467, 531321, 19]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
- dual of repetition code with length 26 [i]
- linear OA(31, 26, F3, 1) (dual of [26, 25, 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
- construction X4 applied to Ce(18) ⊂ Ce(15) [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(3150, 177157, F3, 3, 18) (dual of [(177157, 3), 531321, 19]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3148, 177156, F3, 3, 18) (dual of [(177156, 3), 531320, 19]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3147, 177156, F3, 4, 18) (dual of [(177156, 4), 708477, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3147, 177156, F3, 5, 18) (dual of [(177156, 5), 885633, 19]-NRT-code) | [i] | ||
| 5 | Digital (129, 147, 177156)-net over F3 | [i] | ||