Information on Result #1201304
Digital (55, 68, 1441823)-net over F64, using net defined by OOA based on linear OOA(6468, 1441823, F64, 15, 13) (dual of [(1441823, 15), 21627277, 14]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6468, 2883647, F64, 3, 13) (dual of [(2883647, 3), 8650873, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6468, 2883648, F64, 3, 13) (dual of [(2883648, 3), 8650876, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6419, 87447, F64, 3, 6) (dual of [(87447, 3), 262322, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;192,64) [i]
- linear OOA(6416, 87382, F64, 3, 6) (dual of [(87382, 3), 262130, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6416, 262146, F64, 6) (dual of [262146, 262130, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- OOA 3-folding [i] based on linear OA(6416, 262146, F64, 6) (dual of [262146, 262130, 7]-code), using
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6449, 2796201, F64, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6449, large, F64, 13) (dual of [large, large−49, 14]-code), using
- linear OOA(6419, 87447, F64, 3, 6) (dual of [(87447, 3), 262322, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(6468, 2883648, F64, 3, 13) (dual of [(2883648, 3), 8650876, 14]-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.