Information on Result #1714176
Digital (87, 106, 1648)-net over F3, using net defined by OOA based on linear OOA(3106, 1648, F3, 25, 19) (dual of [(1648, 25), 41094, 20]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3106, 3297, F3, 5, 19) (dual of [(3297, 5), 16379, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3106, 3297, F3, 2, 19) (dual of [(3297, 2), 6488, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3106, 6594, F3, 19) (dual of [6594, 6488, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, 6595, F3, 19) (dual of [6595, 6489, 20]-code), using
- construction XX applied to Ce(18) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- linear OA(397, 6561, F3, 19) (dual of [6561, 6464, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(365, 6561, F3, 13) (dual of [6561, 6496, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(38, 33, F3, 4) (dual of [33, 25, 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
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(18) ⊂ Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3106, 6595, F3, 19) (dual of [6595, 6489, 20]-code), using
- OOA 2-folding [i] based on linear OA(3106, 6594, F3, 19) (dual of [6594, 6488, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3106, 3297, F3, 2, 19) (dual of [(3297, 2), 6488, 20]-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.