Information on Result #679201
Linear OA(4137, 16429, F4, 24) (dual of [16429, 16292, 25]-code), using construction X applied to Ce(24) ⊂ Ce(17) 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(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-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 OA(4138, 16430, F4, 24) (dual of [16430, 16292, 25]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4137, 15889, F4, 2, 24) (dual of [(15889, 2), 31641, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4137, 15889, F4, 3, 24) (dual of [(15889, 3), 47530, 25]-NRT-code) | [i] | ||
| 4 | Digital (113, 137, 15889)-net over F4 | [i] | ||
| 5 | Linear OA(4138, 16431, F4, 24) (dual of [16431, 16293, 25]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(4139, 16433, F4, 24) (dual of [16433, 16294, 25]-code) | [i] | ||
| 7 | Linear OOA(4137, 8214, F4, 2, 24) (dual of [(8214, 2), 16291, 25]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(4137, 5476, F4, 3, 24) (dual of [(5476, 3), 16291, 25]-NRT-code) | [i] | ||
| 9 | Linear OOA(4137, 1369, F4, 24, 24) (dual of [(1369, 24), 32719, 25]-NRT-code) | [i] | OA Folding and Stacking | |