Information on Result #679178
Linear OA(4256, 16429, F4, 47) (dual of [16429, 16173, 48]-code), using construction X applied to Ce(46) ⊂ Ce(40) based on
- linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(4257, 16430, F4, 47) (dual of [16430, 16173, 48]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4258, 16431, F4, 47) (dual of [16431, 16173, 48]-code) | [i] | ||
| 3 | Linear OA(4259, 16432, F4, 47) (dual of [16432, 16173, 48]-code) | [i] | ||
| 4 | Linear OA(4260, 16433, F4, 47) (dual of [16433, 16173, 48]-code) | [i] | ||
| 5 | Linear OOA(4256, 15125, F4, 2, 47) (dual of [(15125, 2), 29994, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(4256, 15125, F4, 3, 47) (dual of [(15125, 3), 45119, 48]-NRT-code) | [i] | ||
| 7 | Digital (209, 256, 15125)-net over F4 | [i] | ||
| 8 | Linear OA(4258, 16432, F4, 47) (dual of [16432, 16174, 48]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(4259, 16434, F4, 47) (dual of [16434, 16175, 48]-code) | [i] | ||
| 10 | Linear OA(4260, 16436, F4, 47) (dual of [16436, 16176, 48]-code) | [i] | ||
| 11 | Linear OOA(4256, 8214, F4, 2, 47) (dual of [(8214, 2), 16172, 48]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(4256, 5476, F4, 3, 47) (dual of [(5476, 3), 16172, 48]-NRT-code) | [i] | ||