Information on Result #1536549
Linear OOA(4126, 38179, F4, 3, 20) (dual of [(38179, 3), 114411, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4126, 38179, F4, 20) (dual of [38179, 38053, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4126, 65565, F4, 20) (dual of [65565, 65439, 21]-code), using
- strength reduction [i] based on linear OA(4126, 65565, F4, 21) (dual of [65565, 65439, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] 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(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(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- strength reduction [i] based on linear OA(4126, 65565, F4, 21) (dual of [65565, 65439, 22]-code), using
Mode: 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 OOA(4126, 9544, F4, 27, 20) (dual of [(9544, 27), 257562, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |