Information on Result #1022141
Linear OOA(6448, 5596608, F64, 3, 8) (dual of [(5596608, 3), 16789776, 9]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(640, s, F64, 3, 0) for arbitrarily large s, using
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(640, 87447, F64, 3, 0) (dual of [(87447, 3), 262341, 1]-NRT-code) (see above)
- linear OOA(641, 87447, F64, 3, 1) (dual of [(87447, 3), 262340, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(641, s, F64, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(641, s, F64, 3, 1) for arbitrarily large s, using
- linear OOA(641, 87447, F64, 3, 1) (dual of [(87447, 3), 262340, 2]-NRT-code) (see above)
- linear OOA(641, 87447, F64, 3, 1) (dual of [(87447, 3), 262340, 2]-NRT-code) (see above)
- linear OOA(641, 87447, F64, 3, 1) (dual of [(87447, 3), 262340, 2]-NRT-code) (see above)
- linear OOA(644, 87447, F64, 3, 2) (dual of [(87447, 3), 262337, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(644, 266305, F64, 3, 2) (dual of [(266305, 3), 798911, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(644, 266305, F64, 2, 2) (dual of [(266305, 2), 532606, 3]-NRT-code), using
- appending kth column [i] based on linear OA(644, 266305, F64, 2) (dual of [266305, 266301, 3]-code), using
- Hamming code H(4,64) [i]
- appending kth column [i] based on linear OA(644, 266305, F64, 2) (dual of [266305, 266301, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(644, 266305, F64, 2, 2) (dual of [(266305, 2), 532606, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(644, 266305, F64, 3, 2) (dual of [(266305, 3), 798911, 3]-NRT-code), using
- linear OOA(644, 87447, F64, 3, 2) (dual of [(87447, 3), 262337, 3]-NRT-code) (see above)
- linear OOA(6410, 87447, F64, 3, 4) (dual of [(87447, 3), 262331, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(647, 262144, F64, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 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(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(6410, 131073, F64, 3, 4) (dual of [(131073, 3), 393209, 5]-NRT-code), using
- linear OOA(6426, 87447, F64, 3, 8) (dual of [(87447, 3), 262315, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(644, 65, F64, 3, 4) (dual of [(65, 3), 191, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;191,64) [i]
- linear OOA(6422, 87382, F64, 3, 8) (dual of [(87382, 3), 262124, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6422, 262146, F64, 8) (dual of [262146, 262124, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6422, 262147, F64, 8) (dual of [262147, 262125, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code) (see above)
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(6422, 262147, F64, 8) (dual of [262147, 262125, 9]-code), using
- OOA 3-folding [i] based on linear OA(6422, 262146, F64, 8) (dual of [262146, 262124, 9]-code), using
- linear OOA(644, 65, F64, 3, 4) (dual of [(65, 3), 191, 5]-NRT-code), 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.
Other Results with Identical Parameters
None.
Depending Results
None.