Information on Result #678760
Linear OA(4171, 65586, F4, 27) (dual of [65586, 65415, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(4172, 65587, F4, 27) (dual of [65587, 65415, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4173, 65588, F4, 27) (dual of [65588, 65415, 28]-code) | [i] | ||
| 3 | Linear OA(4174, 65589, F4, 27) (dual of [65589, 65415, 28]-code) | [i] | ||
| 4 | Linear OA(4175, 65590, F4, 27) (dual of [65590, 65415, 28]-code) | [i] | ||
| 5 | Linear OA(4176, 65591, F4, 27) (dual of [65591, 65415, 28]-code) | [i] | ||
| 6 | Linear OA(4174, 65590, F4, 27) (dual of [65590, 65416, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4175, 65592, F4, 27) (dual of [65592, 65417, 28]-code) | [i] | ||
| 8 | Linear OA(4176, 65594, F4, 27) (dual of [65594, 65418, 28]-code) | [i] | ||
| 9 | Linear OOA(4171, 32793, F4, 2, 27) (dual of [(32793, 2), 65415, 28]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4171, 21862, F4, 3, 27) (dual of [(21862, 3), 65415, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(4171, 5045, F4, 27, 27) (dual of [(5045, 27), 136044, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |