Information on Result #1199284
Digital (70, 83, 1572864)-net over F32, using net defined by OOA based on linear OOA(3283, 1572864, F32, 14, 13) (dual of [(1572864, 14), 22020013, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3283, 4718593, F32, 2, 13) (dual of [(4718593, 2), 9437103, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3283, 4718594, F32, 2, 13) (dual of [(4718594, 2), 9437105, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3222, 524293, F32, 2, 6) (dual of [(524293, 2), 1048564, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3222, 1048586, F32, 6) (dual of [1048586, 1048564, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [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(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(329, 10, F32, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,32)), using
- dual of repetition code with length 10 [i]
- linear OA(321, 10, F32, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(3222, 1048586, F32, 6) (dual of [1048586, 1048564, 7]-code), using
- 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(3222, 524293, F32, 2, 6) (dual of [(524293, 2), 1048564, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3283, 4718594, F32, 2, 13) (dual of [(4718594, 2), 9437105, 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.