Information on Result #2242743
Linear OA(4125, 65564, F4, 20) (dual of [65564, 65439, 21]-code), using 1 times truncation based on linear OA(4126, 65565, F4, 21) (dual of [65565, 65439, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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
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(4125, 35348, F4, 2, 20) (dual of [(35348, 2), 70571, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4125, 35348, F4, 3, 20) (dual of [(35348, 3), 105919, 21]-NRT-code) | [i] | ||
| 3 | Digital (105, 125, 35348)-net over F4 | [i] | ||
| 4 | Linear OOA(4125, 32782, F4, 2, 20) (dual of [(32782, 2), 65439, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4125, 21854, F4, 3, 20) (dual of [(21854, 3), 65437, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(4125, 6556, F4, 20, 20) (dual of [(6556, 20), 130995, 21]-NRT-code) | [i] | OA Folding and Stacking | |