Information on Result #1228133
Digital (61, 72, 5452600)-net over F128, using (u, u+v)-construction based on
- digital (12, 17, 4194301)-net over F128, using
- net defined by OOA [i] based on linear OOA(12817, 4194301, F128, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(12817, 4194301, F128, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12817, large, F128, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(12817, large, F128, 5) (dual of [large, large−17, 6]-code), using
- appending kth column [i] based on linear OOA(12817, 4194301, F128, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12817, 4194301, F128, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
- digital (44, 55, 2726300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (9, 14, 1048580)-net over F128, using
- net defined by OOA [i] based on linear OOA(12814, 1048580, F128, 5, 5) (dual of [(1048580, 5), 5242886, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(12814, 1048580, F128, 4, 5) (dual of [(1048580, 4), 4194306, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12814, 2097161, F128, 5) (dual of [2097161, 2097147, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1287, 2097153, F128, 3) (dual of [2097153, 2097146, 4]-code or 2097153-cap in PG(6,128)), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [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 C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(12814, 2097161, F128, 5) (dual of [2097161, 2097147, 6]-code), using
- appending kth column [i] based on linear OOA(12814, 1048580, F128, 4, 5) (dual of [(1048580, 4), 4194306, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12814, 1048580, F128, 5, 5) (dual of [(1048580, 5), 5242886, 6]-NRT-code), using
- digital (30, 41, 1677720)-net over F128, using
- net defined by OOA [i] based on linear OOA(12841, 1677720, F128, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12841, 8388601, F128, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12841, 8388601, F128, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(12841, 1677720, F128, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- digital (9, 14, 1048580)-net over F128, using
- (u, u+v)-construction [i] based on
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.