Information on Result #1537572
Linear OOA(4145, 32772, F4, 3, 24) (dual of [(32772, 3), 98171, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4145, 32772, F4, 2, 24) (dual of [(32772, 2), 65399, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 65544, F4, 24) (dual of [65544, 65399, 25]-code), using
- 1 times truncation [i] based on linear OA(4146, 65545, F4, 25) (dual of [65545, 65399, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 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(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(4146, 65545, F4, 25) (dual of [65545, 65399, 26]-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(4145, 8192, F4, 27, 24) (dual of [(8192, 27), 221039, 25]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |