Information on Result #1021724
Linear OOA(764, 7792683, F7, 3, 6) (dual of [(7792683, 3), 23377985, 7]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(70, 960800, F7, 3, 0) (dual of [(960800, 3), 2882400, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(70, s, F7, 3, 0) for arbitrarily large s, using
- linear OOA(71, 960800, F7, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(71, s, F7, 3, 1) for arbitrarily large s, using
- linear OOA(71, 960800, F7, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
- linear OOA(71, 960800, F7, 3, 1) (dual of [(960800, 3), 2882399, 2]-NRT-code) (see above)
- linear OOA(78, 960800, F7, 3, 2) (dual of [(960800, 3), 2882392, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(78, 960800, F7, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
- appending kth column [i] based on linear OA(78, 960800, F7, 2) (dual of [960800, 960792, 3]-code), using
- Hamming code H(8,7) [i]
- appending kth column [i] based on linear OA(78, 960800, F7, 2) (dual of [960800, 960792, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(78, 960800, F7, 2, 2) (dual of [(960800, 2), 1921592, 3]-NRT-code), using
- linear OOA(712, 1067080, F7, 3, 3) (dual of [(1067080, 3), 3201228, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(712, 1067080, F7, 2, 3) (dual of [(1067080, 2), 2134148, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(712, 1067080, F7, 3) (dual of [1067080, 1067068, 4]-code or 1067080-cap in PG(11,7)), using
- appending kth column [i] based on linear OOA(712, 1067080, F7, 2, 3) (dual of [(1067080, 2), 2134148, 4]-NRT-code), using
- linear OOA(741, 1921603, F7, 3, 6) (dual of [(1921603, 3), 5764768, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(741, 5764809, F7, 6) (dual of [5764809, 5764768, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(741, 5764801, F7, 6) (dual of [5764801, 5764760, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(733, 5764801, F7, 5) (dual of [5764801, 5764768, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OOA 3-folding [i] based on linear OA(741, 5764809, F7, 6) (dual of [5764809, 5764768, 7]-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.
Other Results with Identical Parameters
None.
Depending Results
None.