Information on Result #1199288
Digital (72, 85, 1572874)-net over F32, using net defined by OOA based on linear OOA(3285, 1572874, F32, 14, 13) (dual of [(1572874, 14), 22020151, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3285, 4718623, F32, 2, 13) (dual of [(4718623, 2), 9437161, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3285, 4718624, F32, 2, 13) (dual of [(4718624, 2), 9437163, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3224, 524323, F32, 2, 6) (dual of [(524323, 2), 1048622, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(323, 33, F32, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;63,32) [i]
- linear OOA(3221, 524290, F32, 2, 6) (dual of [(524290, 2), 1048559, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OOA 2-folding [i] based on linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using
- linear OOA(323, 33, F32, 2, 3) (dual of [(33, 2), 63, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3261, 4194301, F32, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(3261, 8388602, F32, 13) (dual of [8388602, 8388541, 14]-code), using
- linear OOA(3224, 524323, F32, 2, 6) (dual of [(524323, 2), 1048622, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3285, 4718624, F32, 2, 13) (dual of [(4718624, 2), 9437163, 14]-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
None.