Information on Result #678756
Linear OA(4195, 65586, F4, 31) (dual of [65586, 65391, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(4196, 65587, F4, 31) (dual of [65587, 65391, 32]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4197, 65588, F4, 31) (dual of [65588, 65391, 32]-code) | [i] | ||
| 3 | Linear OA(4198, 65589, F4, 31) (dual of [65589, 65391, 32]-code) | [i] | ||
| 4 | Linear OA(4199, 65590, F4, 31) (dual of [65590, 65391, 32]-code) | [i] | ||
| 5 | Linear OA(4200, 65591, F4, 31) (dual of [65591, 65391, 32]-code) | [i] | ||
| 6 | Linear OOA(4195, 41432, F4, 2, 31) (dual of [(41432, 2), 82669, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4195, 41432, F4, 3, 31) (dual of [(41432, 3), 124101, 32]-NRT-code) | [i] | ||
| 8 | Digital (164, 195, 41432)-net over F4 | [i] | ||
| 9 | Linear OA(4198, 65590, F4, 31) (dual of [65590, 65392, 32]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4199, 65592, F4, 31) (dual of [65592, 65393, 32]-code) | [i] | ||
| 11 | Linear OA(4200, 65594, F4, 31) (dual of [65594, 65394, 32]-code) | [i] | ||
| 12 | Linear OOA(4195, 32793, F4, 2, 31) (dual of [(32793, 2), 65391, 32]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(4195, 21862, F4, 3, 31) (dual of [(21862, 3), 65391, 32]-NRT-code) | [i] | ||
| 14 | Linear OOA(4195, 4372, F4, 31, 31) (dual of [(4372, 31), 135337, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |