Information on Result #1716904
Digital (189, 226, 2345)-net over F3, using net defined by OOA based on linear OOA(3226, 2345, F3, 45, 37) (dual of [(2345, 45), 105299, 38]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(3226, 9381, F3, 5, 37) (dual of [(9381, 5), 46679, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3226, 9382, F3, 5, 37) (dual of [(9382, 5), 46684, 38]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3226, 9382, F3, 2, 37) (dual of [(9382, 2), 18538, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3226, 9859, F3, 2, 37) (dual of [(9859, 2), 19492, 38]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3225, 9859, F3, 2, 37) (dual of [(9859, 2), 19493, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3225, 19718, F3, 37) (dual of [19718, 19493, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(31) [i] based on
- linear OA(3217, 19683, F3, 37) (dual of [19683, 19466, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(38, 35, F3, 4) (dual of [35, 27, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(36) ⊂ Ce(31) [i] based on
- OOA 2-folding [i] based on linear OA(3225, 19718, F3, 37) (dual of [19718, 19493, 38]-code), using
- 31 times duplication [i] based on linear OOA(3225, 9859, F3, 2, 37) (dual of [(9859, 2), 19493, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3226, 9859, F3, 2, 37) (dual of [(9859, 2), 19492, 38]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3226, 9382, F3, 2, 37) (dual of [(9382, 2), 18538, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3226, 9382, F3, 5, 37) (dual of [(9382, 5), 46684, 38]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.