Information on Result #1537753
Linear OOA(4148, 1551289, F4, 3, 18) (dual of [(1551289, 3), 4653719, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4148, 1551289, F4, 2, 18) (dual of [(1551289, 2), 3102430, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4148, 2097165, F4, 2, 18) (dual of [(2097165, 2), 4194182, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4148, 4194330, F4, 18) (dual of [4194330, 4194182, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(44, 26, F4, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- construction X applied to Ce(17) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(4148, 4194330, F4, 18) (dual of [4194330, 4194182, 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(4148, 517096, F4, 21, 18) (dual of [(517096, 21), 10858868, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |