Information on Result #679634
Linear OA(4172, 4111, F4, 38) (dual of [4111, 3939, 39]-code), using construction X applied to Ce(37) ⊂ Ce(34) based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(43, 15, F4, 2) (dual of [15, 12, 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(4172, 3418, F4, 2, 38) (dual of [(3418, 2), 6664, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4172, 3418, F4, 3, 38) (dual of [(3418, 3), 10082, 39]-NRT-code) | [i] | ||
| 3 | Digital (134, 172, 3418)-net over F4 | [i] | ||
| 4 | Linear OOA(4172, 2055, F4, 2, 38) (dual of [(2055, 2), 3938, 39]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4172, 1370, F4, 3, 38) (dual of [(1370, 3), 3938, 39]-NRT-code) | [i] | ||