Information on Result #1061174
Linear OOA(3227, 1195750, F3, 4, 24) (dual of [(1195750, 4), 4782773, 25]-NRT-code), using OOA 4-folding based on linear OA(3227, 4783000, F3, 24) (dual of [4783000, 4782773, 25]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3226, 4782999, F3, 24) (dual of [4782999, 4782773, 25]-code), using
- construction X4 applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 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(24) ⊂ Ce(21) [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(3228, 1195750, F3, 4, 24) (dual of [(1195750, 4), 4782772, 25]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3227, 1195750, F3, 5, 24) (dual of [(1195750, 5), 5978523, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (203, 227, 1195750)-net over F3 | [i] | ||