Information on Result #678766
Linear OA(4134, 65589, F4, 21) (dual of [65589, 65455, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
- 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(481, 65536, F4, 14) (dual of [65536, 65455, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(4135, 65590, F4, 21) (dual of [65590, 65455, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4133, 65588, F4, 20) (dual of [65588, 65455, 21]-code) | [i] | Truncation | |
| 3 | Linear OOA(4134, 32794, F4, 2, 21) (dual of [(32794, 2), 65454, 22]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4134, 21863, F4, 3, 21) (dual of [(21863, 3), 65455, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(4134, 6558, F4, 21, 21) (dual of [(6558, 21), 137584, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |