Information on Result #1191592
Digital (112, 124, 2883584)-net over F8, using net defined by OOA based on linear OOA(8124, 2883584, F8, 15, 12) (dual of [(2883584, 15), 43253636, 13]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8124, 5767169, F8, 3, 12) (dual of [(5767169, 3), 17301383, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8124, 5767170, F8, 3, 12) (dual of [(5767170, 3), 17301386, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(834, 174768, F8, 3, 6) (dual of [(174768, 3), 524270, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(834, 524304, F8, 6) (dual of [524304, 524270, 7]-code), using
- trace code [i] based on linear OA(6417, 262152, F64, 6) (dual of [262152, 262135, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [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(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, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(6417, 262152, F64, 6) (dual of [262152, 262135, 7]-code), using
- OOA 3-folding [i] based on linear OA(834, 524304, F8, 6) (dual of [524304, 524270, 7]-code), using
- linear OOA(890, 5592402, F8, 3, 12) (dual of [(5592402, 3), 16777116, 13]-NRT-code), using
- trace code [i] based on linear OOA(6445, 2796201, F64, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- trace code [i] based on linear OOA(6445, 2796201, F64, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- linear OOA(834, 174768, F8, 3, 6) (dual of [(174768, 3), 524270, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8124, 5767170, F8, 3, 12) (dual of [(5767170, 3), 17301386, 13]-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.