Information on Result #823330
Linear OOA(4126, 524305, F4, 2, 17) (dual of [(524305, 2), 1048484, 18]-NRT-code), using OOA 2-folding based on linear OA(4126, 1048610, F4, 17) (dual of [1048610, 1048484, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4126, 1048611, F4, 17) (dual of [1048611, 1048485, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [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(4126, 524305, F4, 2, 16) (dual of [(524305, 2), 1048484, 17]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4126, 433368, F4, 3, 17) (dual of [(433368, 3), 1299978, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (109, 126, 433368)-net over F4 | [i] | ||