Information on Result #2242858
Linear OA(4127, 65567, F4, 20) (dual of [65567, 65440, 21]-code), using 1 times truncation based on linear OA(4128, 65568, F4, 21) (dual of [65568, 65440, 22]-code), using
- construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(14) [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(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-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
- linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(4127, 41236, F4, 2, 20) (dual of [(41236, 2), 82345, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4127, 41236, F4, 3, 20) (dual of [(41236, 3), 123581, 21]-NRT-code) | [i] | ||
| 3 | Digital (107, 127, 41236)-net over F4 | [i] | ||