Information on Result #3178623
Digital (53, 56, large)-net over F128, using 6 times m-reduction based on digital (53, 62, large)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (9, 13, 4194301)-net over F128, using
- net defined by OOA [i] based on linear OOA(12813, 4194301, F128, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12813, 8388602, F128, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12813, large, F128, 4) (dual of [large, large−13, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(12813, large, F128, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12813, 8388602, F128, 4) (dual of [8388602, 8388589, 5]-code), using
- net defined by OOA [i] based on linear OOA(12813, 4194301, F128, 4, 4) (dual of [(4194301, 4), 16777191, 5]-NRT-code), using
- digital (40, 49, 7242231)-net over F128, using
- net defined by OOA [i] based on linear OOA(12849, 7242231, F128, 12, 9) (dual of [(7242231, 12), 86906723, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(12849, 7242232, F128, 4, 9) (dual of [(7242232, 4), 28968879, 10]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1280, s, F128, 4, 0) for arbitrarily large s, using
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code) (see above)
- linear OOA(1281, 49156, F128, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 4, 1) for arbitrarily large s, using
- appending 3 arbitrary columns [i] based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 4, 1) for arbitrarily large s, using
- linear OOA(1281, 49156, F128, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
- linear OOA(1281, 49156, F128, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
- linear OOA(1281, 49156, F128, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
- linear OOA(1281, 49156, F128, 4, 1) (dual of [(49156, 4), 196623, 2]-NRT-code) (see above)
- linear OOA(1284, 49156, F128, 4, 2) (dual of [(49156, 4), 196620, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- Hamming code H(4,128) [i]
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
- linear OOA(1285, 49156, F128, 4, 3) (dual of [(49156, 4), 196619, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1285, 49156, F128, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1285, 49156, F128, 2, 3) (dual of [(49156, 2), 98307, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1285, 49156, F128, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
- linear OOA(12810, 524288, F128, 4, 4) (dual of [(524288, 4), 2097142, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [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(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(12810, 1048577, F128, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
- linear OOA(12825, 524288, F128, 4, 9) (dual of [(524288, 4), 2097127, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 4-folding [i] based on linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using
- linear OOA(1280, 49156, F128, 4, 0) (dual of [(49156, 4), 196624, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(12849, 7242232, F128, 4, 9) (dual of [(7242232, 4), 28968879, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12849, 7242231, F128, 12, 9) (dual of [(7242231, 12), 86906723, 10]-NRT-code), using
- digital (9, 13, 4194301)-net over F128, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.