Information on Result #1324090
Linear OA(4213, 16443, F4, 38) (dual of [16443, 16230, 39]-code), using construction X with Varšamov bound based on
- linear OA(4211, 16440, F4, 38) (dual of [16440, 16229, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(29) [i] based on
- linear OA(4197, 16384, F4, 38) (dual of [16384, 16187, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(37) ⊂ Ce(29) [i] based on
- linear OA(4211, 16441, F4, 36) (dual of [16441, 16230, 37]-code), using Gilbert–Varšamov bound and bm = 4211 > Vbs−1(k−1) = 16832 731012 862313 375188 289858 007738 261175 479441 680261 835866 924029 230359 202856 222136 794578 244895 084752 531184 407823 879814 950211 [i]
- linear OA(41, 2, F4, 1) (dual of [2, 1, 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(4213, 16443, F4, 2, 38) (dual of [(16443, 2), 32673, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4213, 16443, F4, 3, 38) (dual of [(16443, 3), 49116, 39]-NRT-code) | [i] | ||
| 3 | Digital (175, 213, 16443)-net over F4 | [i] | ||