Information on Result #822707
Linear OOA(466, 524305, F4, 2, 9) (dual of [(524305, 2), 1048544, 10]-NRT-code), using OOA 2-folding based on linear OA(466, 1048610, F4, 9) (dual of [1048610, 1048544, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(466, 1048611, F4, 9) (dual of [1048611, 1048545, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(4) [i] based on
- linear OA(461, 1048576, F4, 9) (dual of [1048576, 1048515, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-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(8) ⊂ Ce(4) [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(466, 524305, F4, 3, 9) (dual of [(524305, 3), 1572849, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (57, 66, 524305)-net over F4 | [i] | ||