Information on Result #1203442
Digital (65, 77, 3320490)-net over F128, using net defined by OOA based on linear OOA(12877, 3320490, F128, 15, 12) (dual of [(3320490, 15), 49807273, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(12877, 6640981, F128, 3, 12) (dual of [(6640981, 3), 19922866, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12877, 6640982, F128, 3, 12) (dual of [(6640982, 3), 19922869, 13]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(12811, 1048580, F128, 3, 4) (dual of [(1048580, 3), 3145729, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12811, 2097160, F128, 4) (dual of [2097160, 2097149, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- 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(1284, 2097152, F128, 2) (dual of [2097152, 2097148, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [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(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(12811, 2097160, F128, 4) (dual of [2097160, 2097149, 5]-code), using
- linear OOA(12821, 2796201, F128, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- linear OOA(12845, 2796201, F128, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- linear OOA(12811, 1048580, F128, 3, 4) (dual of [(1048580, 3), 3145729, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(12877, 6640982, F128, 3, 12) (dual of [(6640982, 3), 19922869, 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.