Information on Result #823946
Linear OOA(4177, 524306, F4, 2, 23) (dual of [(524306, 2), 1048435, 24]-NRT-code), using OOA 2-folding based on linear OA(4177, 1048612, F4, 23) (dual of [1048612, 1048435, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4176, 1048611, F4, 23) (dual of [1048611, 1048435, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4141, 1048576, F4, 19) (dual of [1048576, 1048435, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(22) ⊂ Ce(18) [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(4177, 513094, F4, 3, 23) (dual of [(513094, 3), 1539105, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (154, 177, 513094)-net over F4 | [i] | ||