Information on Result #679070
Linear OA(4221, 16401, F4, 42) (dual of [16401, 16180, 43]-code), using construction X applied to Ce(41) ⊂ Ce(38) based on
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(43, 17, F4, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), 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(4221, 10733, F4, 2, 42) (dual of [(10733, 2), 21245, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4221, 10733, F4, 3, 42) (dual of [(10733, 3), 31978, 43]-NRT-code) | [i] | ||
| 3 | Digital (179, 221, 10733)-net over F4 | [i] | ||
| 4 | Linear OOA(4221, 8200, F4, 2, 42) (dual of [(8200, 2), 16179, 43]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4221, 5467, F4, 3, 42) (dual of [(5467, 3), 16180, 43]-NRT-code) | [i] | ||