Information on Result #1768311
Digital (187, 205, 4194369)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3205, 4194369, F3, 2, 18) (dual of [(4194369, 2), 8388533, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(325, 68, F3, 2, 9) (dual of [(68, 2), 111, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(325, 68, F3, 9) (dual of [68, 43, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(325, 80, F3, 9) (dual of [80, 55, 10]-code), using
- the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,53}, and minimum distance d ≥ |{−1,0,…,7}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(325, 80, F3, 9) (dual of [80, 55, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(325, 68, F3, 9) (dual of [68, 43, 10]-code), using
- linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- linear OOA(325, 68, F3, 2, 9) (dual of [(68, 2), 111, 10]-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.