Information on Result #678765
Linear OA(4142, 65589, F4, 22) (dual of [65589, 65447, 23]-code), using construction X applied to Ce(21) ⊂ Ce(14) based on
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(413, 53, F4, 6) (dual of [53, 40, 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(4143, 65590, F4, 22) (dual of [65590, 65447, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4144, 65591, F4, 22) (dual of [65591, 65447, 23]-code) | [i] | ||
| 3 | Linear OA(4144, 65592, F4, 22) (dual of [65592, 65448, 23]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OOA(4142, 32794, F4, 2, 22) (dual of [(32794, 2), 65446, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4142, 21863, F4, 3, 22) (dual of [(21863, 3), 65447, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(4142, 5962, F4, 22, 22) (dual of [(5962, 22), 131022, 23]-NRT-code) | [i] | OA Folding and Stacking | |