Information on Result #825881
Linear OOA(4206, 8221, F4, 2, 37) (dual of [(8221, 2), 16236, 38]-NRT-code), using OOA 2-folding based on linear OA(4206, 16442, F4, 37) (dual of [16442, 16236, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-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(4206, 8221, F4, 2, 36) (dual of [(8221, 2), 16236, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4208, 8222, F4, 2, 37) (dual of [(8222, 2), 16236, 38]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(4207, 8221, F4, 2, 37) (dual of [(8221, 2), 16235, 38]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(4205, 8220, F4, 2, 36) (dual of [(8220, 2), 16235, 37]-NRT-code) | [i] | Truncation for OOAs | |