Information on Result #1203870
Digital (37, 57, 1715)-net over F128, using net defined by OOA based on linear OOA(12857, 1715, F128, 22, 20) (dual of [(1715, 22), 37673, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(12857, 8576, F128, 2, 20) (dual of [(8576, 2), 17095, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12857, 8580, F128, 2, 20) (dual of [(8580, 2), 17103, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12818, 387, F128, 2, 10) (dual of [(387, 2), 756, 11]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(1283, 129, F128, 2, 3) (dual of [(129, 2), 255, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;255,128) [i]
- linear OOA(1285, 129, F128, 2, 5) (dual of [(129, 2), 253, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;253,128) [i]
- linear OOA(12810, 129, F128, 2, 10) (dual of [(129, 2), 248, 11]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;248,128) [i]
- linear OOA(1283, 129, F128, 2, 3) (dual of [(129, 2), 255, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(12839, 8193, F128, 2, 20) (dual of [(8193, 2), 16347, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12839, 16386, F128, 20) (dual of [16386, 16347, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(12839, 16386, F128, 20) (dual of [16386, 16347, 21]-code), using
- linear OOA(12818, 387, F128, 2, 10) (dual of [(387, 2), 756, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(12857, 8580, F128, 2, 20) (dual of [(8580, 2), 17103, 21]-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.