Information on Result #1203416
Digital (50, 62, 1747626)-net over F128, using net defined by OOA based on linear OOA(12862, 1747626, F128, 14, 12) (dual of [(1747626, 14), 24466702, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(12862, 5242879, F128, 2, 12) (dual of [(5242879, 2), 10485696, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12862, 5242881, F128, 2, 12) (dual of [(5242881, 2), 10485700, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(12817, 1048580, F128, 2, 6) (dual of [(1048580, 2), 2097143, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12817, 2097160, F128, 6) (dual of [2097160, 2097143, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 8, F128, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
- dual of repetition code with length 8 [i]
- linear OA(1281, 8, F128, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- Reed–Solomon code RS(127,128) [i]
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(12817, 2097160, F128, 6) (dual of [2097160, 2097143, 7]-code), using
- linear OOA(12845, 4194301, F128, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12845, 8388602, F128, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(12845, 8388602, F128, 12) (dual of [8388602, 8388557, 13]-code), using
- linear OOA(12817, 1048580, F128, 2, 6) (dual of [(1048580, 2), 2097143, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(12862, 5242881, F128, 2, 12) (dual of [(5242881, 2), 10485700, 13]-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.