Information on Result #1545733
Linear OOA(4249, 16445, F4, 3, 45) (dual of [(16445, 3), 49086, 46]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4249, 16445, F4, 45) (dual of [16445, 16196, 46]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4246, 16440, F4, 45) (dual of [16440, 16194, 46]-code), using
- construction X applied to Ce(44) ⊂ Ce(36) [i] based on
- linear OA(4232, 16384, F4, 45) (dual of [16384, 16152, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4190, 16384, F4, 37) (dual of [16384, 16194, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(44) ⊂ Ce(36) [i] based on
- linear OA(4246, 16442, F4, 43) (dual of [16442, 16196, 44]-code), using Gilbert–Varšamov bound and bm = 4246 > Vbs−1(k−1) = 86 697833 185116 284300 590827 640063 084176 888237 431648 913177 580174 273571 403649 739246 386107 088928 384677 334662 587947 817038 965171 887227 218438 106111 511952 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 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
- linear OA(4246, 16440, F4, 45) (dual of [16440, 16194, 46]-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(4249, 2055, F4, 51, 45) (dual of [(2055, 51), 104556, 46]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |