Information on Result #678764
Linear OA(4147, 65586, F4, 23) (dual of [65586, 65439, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 50, F4, 5) (dual of [50, 40, 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(4148, 65587, F4, 23) (dual of [65587, 65439, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4149, 65588, F4, 23) (dual of [65588, 65439, 24]-code) | [i] | ||
| 3 | Linear OA(4150, 65589, F4, 23) (dual of [65589, 65439, 24]-code) | [i] | ||
| 4 | Linear OA(4151, 65590, F4, 23) (dual of [65590, 65439, 24]-code) | [i] | ||
| 5 | Linear OA(4152, 65591, F4, 23) (dual of [65591, 65439, 24]-code) | [i] | ||
| 6 | Linear OOA(4147, 44357, F4, 2, 23) (dual of [(44357, 2), 88567, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4147, 44357, F4, 3, 23) (dual of [(44357, 3), 132924, 24]-NRT-code) | [i] | ||
| 8 | Digital (124, 147, 44357)-net over F4 | [i] | ||
| 9 | Linear OA(4149, 65589, F4, 23) (dual of [65589, 65440, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4150, 65591, F4, 23) (dual of [65591, 65441, 24]-code) | [i] | ||
| 11 | Linear OA(4151, 65593, F4, 23) (dual of [65593, 65442, 24]-code) | [i] | ||
| 12 | Linear OA(4152, 65595, F4, 23) (dual of [65595, 65443, 24]-code) | [i] | ||
| 13 | Linear OOA(4147, 32793, F4, 2, 23) (dual of [(32793, 2), 65439, 24]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4147, 21862, F4, 3, 23) (dual of [(21862, 3), 65439, 24]-NRT-code) | [i] | ||
| 15 | Linear OOA(4147, 5962, F4, 23, 23) (dual of [(5962, 23), 136979, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |