Information on Result #679202
Linear OA(4130, 16429, F4, 23) (dual of [16429, 16299, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(4131, 16430, F4, 23) (dual of [16430, 16299, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4132, 16431, F4, 23) (dual of [16431, 16299, 24]-code) | [i] | ||
| 3 | Linear OA(4133, 16432, F4, 23) (dual of [16432, 16299, 24]-code) | [i] | ||
| 4 | Linear OA(4134, 16433, F4, 23) (dual of [16433, 16299, 24]-code) | [i] | ||
| 5 | Linear OA(4135, 16434, F4, 23) (dual of [16434, 16299, 24]-code) | [i] | ||
| 6 | Linear OOA(4130, 14429, F4, 2, 23) (dual of [(14429, 2), 28728, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4130, 14429, F4, 3, 23) (dual of [(14429, 3), 43157, 24]-NRT-code) | [i] | ||
| 8 | Digital (107, 130, 14429)-net over F4 | [i] | ||
| 9 | Linear OA(4132, 16432, F4, 23) (dual of [16432, 16300, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4133, 16434, F4, 23) (dual of [16434, 16301, 24]-code) | [i] | ||
| 11 | Linear OA(4134, 16436, F4, 23) (dual of [16436, 16302, 24]-code) | [i] | ||
| 12 | Linear OA(4135, 16438, F4, 23) (dual of [16438, 16303, 24]-code) | [i] | ||
| 13 | Linear OOA(4130, 8214, F4, 2, 23) (dual of [(8214, 2), 16298, 24]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4130, 5476, F4, 3, 23) (dual of [(5476, 3), 16298, 24]-NRT-code) | [i] | ||
| 15 | Linear OOA(4130, 1493, F4, 23, 23) (dual of [(1493, 23), 34209, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |