Information on Result #1201488
Digital (69, 85, 1081344)-net over F64, using net defined by OOA based on linear OOA(6485, 1081344, F64, 18, 16) (dual of [(1081344, 18), 19464107, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(6485, 4325377, F64, 2, 16) (dual of [(4325377, 2), 8650669, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6485, 4325378, F64, 2, 16) (dual of [(4325378, 2), 8650671, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6424, 131077, F64, 2, 8) (dual of [(131077, 2), 262130, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6424, 262154, F64, 8) (dual of [262154, 262130, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6424, 262155, F64, 8) (dual of [262155, 262131, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(6424, 262155, F64, 8) (dual of [262155, 262131, 9]-code), using
- OOA 2-folding [i] based on linear OA(6424, 262154, F64, 8) (dual of [262154, 262130, 9]-code), using
- linear OOA(6461, 4194301, F64, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- OOA 2-folding [i] based on linear OA(6461, 8388602, F64, 16) (dual of [8388602, 8388541, 17]-code), using
- linear OOA(6424, 131077, F64, 2, 8) (dual of [(131077, 2), 262130, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(6485, 4325378, F64, 2, 16) (dual of [(4325378, 2), 8650671, 17]-NRT-code), using
Mode: Constructive and 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (154, 170, 2162688)-net over F8 | [i] | Trace Code for Nets | |