Information on Result #1324180
Linear OA(4237, 16453, F4, 42) (dual of [16453, 16216, 43]-code), using construction X with Varšamov bound based on
- linear OA(4236, 16451, F4, 42) (dual of [16451, 16215, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(32) [i] based on
- linear OA(4218, 16384, F4, 42) (dual of [16384, 16166, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4169, 16384, F4, 33) (dual of [16384, 16215, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(418, 67, F4, 8) (dual of [67, 49, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(418, 68, F4, 8) (dual of [68, 50, 9]-code), using
- construction X applied to Ce(41) ⊂ Ce(32) [i] based on
- linear OA(4236, 16452, F4, 41) (dual of [16452, 16216, 42]-code), using Gilbert–Varšamov bound and bm = 4236 > Vbs−1(k−1) = 63 189110 647489 946867 820065 711473 656328 098403 678493 572772 614151 553585 495328 775078 822302 716940 181130 885155 012569 782978 494346 738607 358686 115560 [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
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(4237, 16453, F4, 2, 42) (dual of [(16453, 2), 32669, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4237, 16453, F4, 3, 42) (dual of [(16453, 3), 49122, 43]-NRT-code) | [i] | ||
| 3 | Digital (195, 237, 16453)-net over F4 | [i] | ||