Information on Result #679198
Linear OA(4151, 16429, F4, 27) (dual of [16429, 16278, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
- linear OA(4141, 16384, F4, 27) (dual of [16384, 16243, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(4152, 16430, F4, 27) (dual of [16430, 16278, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4153, 16431, F4, 27) (dual of [16431, 16278, 28]-code) | [i] | ||
| 3 | Linear OA(4154, 16432, F4, 27) (dual of [16432, 16278, 28]-code) | [i] | ||
| 4 | Linear OA(4155, 16433, F4, 27) (dual of [16433, 16278, 28]-code) | [i] | ||
| 5 | Linear OA(4156, 16434, F4, 27) (dual of [16434, 16278, 28]-code) | [i] | ||
| 6 | Linear OA(4153, 16432, F4, 27) (dual of [16432, 16279, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4154, 16434, F4, 27) (dual of [16434, 16280, 28]-code) | [i] | ||
| 8 | Linear OA(4155, 16436, F4, 27) (dual of [16436, 16281, 28]-code) | [i] | ||
| 9 | Linear OA(4156, 16438, F4, 27) (dual of [16438, 16282, 28]-code) | [i] | ||
| 10 | Linear OOA(4151, 8214, F4, 2, 27) (dual of [(8214, 2), 16277, 28]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(4151, 5476, F4, 3, 27) (dual of [(5476, 3), 16277, 28]-NRT-code) | [i] | ||