Information on Result #1430833
Linear OOA(4220, 16444, F4, 2, 39) (dual of [(16444, 2), 32668, 40]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4220, 16444, F4, 39) (dual of [16444, 16224, 40]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4218, 16440, F4, 39) (dual of [16440, 16222, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(30) [i] based on
- linear OA(4204, 16384, F4, 39) (dual of [16384, 16180, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(38) ⊂ Ce(30) [i] based on
- linear OA(4218, 16442, F4, 38) (dual of [16442, 16224, 39]-code), using Gilbert–Varšamov bound and bm = 4218 > Vbs−1(k−1) = 30677 150176 584088 669507 683963 646940 620101 150064 912773 882772 440054 274121 533020 149443 758716 347565 879824 992530 439843 307047 728117 595244 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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(4218, 16440, F4, 39) (dual of [16440, 16222, 40]-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(4220, 8222, F4, 3, 39) (dual of [(8222, 3), 24446, 40]-NRT-code) | [i] | OOA Folding | |