Information on Result #1324226
Linear OA(4250, 16447, F4, 45) (dual of [16447, 16197, 46]-code), using construction X with Varšamov bound 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, 16443, F4, 43) (dual of [16443, 16197, 44]-code), using Gilbert–Varšamov bound and bm = 4246 > Vbs−1(k−1) = 86 919859 693534 699858 603338 551172 944189 456016 780443 047038 723555 346524 679859 857964 165522 152943 794079 070793 308453 658832 487562 688969 010691 787884 880008 [i]
- linear OA(41, 4, F4, 1) (dual of [4, 3, 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
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(4250, 16447, F4, 2, 45) (dual of [(16447, 2), 32644, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4250, 16447, F4, 3, 45) (dual of [(16447, 3), 49091, 46]-NRT-code) | [i] | ||
| 3 | Digital (205, 250, 16447)-net over F4 | [i] | ||