Information on Result #679344
Linear OA(4134, 16413, F4, 25) (dual of [16413, 16279, 26]-code), using construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) based on
- linear OA(4127, 16384, F4, 25) (dual of [16384, 16257, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-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 OA(4133, 16412, F4, 24) (dual of [16412, 16279, 25]-code) | [i] | Truncation | |
| 2 | Linear OOA(4134, 9506, F4, 2, 25) (dual of [(9506, 2), 18878, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4134, 9506, F4, 3, 25) (dual of [(9506, 3), 28384, 26]-NRT-code) | [i] | ||
| 4 | Digital (109, 134, 9506)-net over F4 | [i] | ||
| 5 | Linear OOA(4134, 5471, F4, 3, 25) (dual of [(5471, 3), 16279, 26]-NRT-code) | [i] | OOA Folding | |