Information on Result #824053
Linear OOA(4182, 524298, F4, 2, 24) (dual of [(524298, 2), 1048414, 25]-NRT-code), using OOA 2-folding based on linear OA(4182, 1048596, F4, 24) (dual of [1048596, 1048414, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 1048597, F4, 24) (dual of [1048597, 1048415, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(41, 21, F4, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X 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(4182, 418667, F4, 3, 24) (dual of [(418667, 3), 1255819, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (158, 182, 418667)-net over F4 | [i] | ||