Information on Result #1536312
Linear OOA(4121, 127923, F4, 3, 18) (dual of [(127923, 3), 383648, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4121, 127923, F4, 2, 18) (dual of [(127923, 2), 255725, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4121, 131082, F4, 2, 18) (dual of [(131082, 2), 262043, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4121, 262164, F4, 18) (dual of [262164, 262043, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, 262165, F4, 18) (dual of [262165, 262044, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4121, 262165, F4, 18) (dual of [262165, 262044, 19]-code), using
- OOA 2-folding [i] based on linear OA(4121, 262164, F4, 18) (dual of [262164, 262043, 19]-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(4121, 42640, F4, 21, 18) (dual of [(42640, 21), 895319, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |