Information on Result #824706
Linear OOA(4175, 32783, F4, 2, 29) (dual of [(32783, 2), 65391, 30]-NRT-code), using OOA 2-folding based on linear OA(4175, 65566, F4, 29) (dual of [65566, 65391, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(28) ⊂ Ce(24) [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(4175, 32783, F4, 2, 28) (dual of [(32783, 2), 65391, 29]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4175, 32783, F4, 3, 29) (dual of [(32783, 3), 98174, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (146, 175, 32783)-net over F4 | [i] | ||