Information on Result #1537806
Linear OOA(4149, 16442, F4, 3, 26) (dual of [(16442, 3), 49177, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4149, 16442, F4, 26) (dual of [16442, 16293, 27]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4148, 16440, F4, 26) (dual of [16440, 16292, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(25) ⊂ Ce(17) [i] based on
- linear OA(4148, 16441, F4, 25) (dual of [16441, 16293, 26]-code), using Gilbert–Varšamov bound and bm = 4148 > Vbs−1(k−1) = 68040 122538 102909 735622 792353 535530 913361 467030 694296 148446 747088 963804 506970 124580 682164 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4148, 16440, F4, 26) (dual of [16440, 16292, 27]-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(4149, 3288, F4, 33, 26) (dual of [(3288, 33), 108355, 27]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |