Information on Result #678597
Linear OA(4206, 65598, F4, 32) (dual of [65598, 65392, 33]-code), using construction X applied to C([0,16]) ⊂ C([0,12]) based on
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-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(4207, 65599, F4, 32) (dual of [65599, 65392, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4210, 65602, F4, 32) (dual of [65602, 65392, 33]-code) | [i] | ||
| 3 | Linear OA(4211, 65603, F4, 32) (dual of [65603, 65392, 33]-code) | [i] | ||
| 4 | Linear OOA(4206, 52185, F4, 2, 32) (dual of [(52185, 2), 104164, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(4206, 52185, F4, 3, 32) (dual of [(52185, 3), 156349, 33]-NRT-code) | [i] | ||
| 6 | Digital (174, 206, 52185)-net over F4 | [i] | ||
| 7 | Linear OA(4208, 65601, F4, 32) (dual of [65601, 65393, 33]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OA(4209, 65603, F4, 32) (dual of [65603, 65394, 33]-code) | [i] | ||
| 9 | Linear OA(4210, 65605, F4, 32) (dual of [65605, 65395, 33]-code) | [i] | ||
| 10 | Linear OA(4211, 65607, F4, 32) (dual of [65607, 65396, 33]-code) | [i] | ||
| 11 | Linear OA(4212, 65609, F4, 32) (dual of [65609, 65397, 33]-code) | [i] | ||
| 12 | Linear OA(4213, 65611, F4, 32) (dual of [65611, 65398, 33]-code) | [i] | ||
| 13 | Linear OOA(4206, 32799, F4, 2, 32) (dual of [(32799, 2), 65392, 33]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4206, 21866, F4, 3, 32) (dual of [(21866, 3), 65392, 33]-NRT-code) | [i] | ||