Information on Result #1196012
Digital (12, 21, 169)-net over F25, using net defined by OOA based on linear OOA(2521, 169, F25, 10, 9) (dual of [(169, 10), 1669, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2521, 339, F25, 2, 9) (dual of [(339, 2), 657, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2521, 340, F25, 2, 9) (dual of [(340, 2), 659, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(254, 26, F25, 2, 4) (dual of [(26, 2), 48, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;48,25) [i]
- linear OOA(2517, 314, F25, 2, 9) (dual of [(314, 2), 611, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2517, 628, F25, 9) (dual of [628, 611, 10]-code), using
- construction XX applied to C1 = C([623,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([623,7]) [i] based on
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2515, 624, F25, 8) (dual of [624, 609, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2517, 624, F25, 9) (dual of [624, 607, 10]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([623,7]) [i] based on
- OOA 2-folding [i] based on linear OA(2517, 628, F25, 9) (dual of [628, 611, 10]-code), using
- linear OOA(254, 26, F25, 2, 4) (dual of [(26, 2), 48, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2521, 340, F25, 2, 9) (dual of [(340, 2), 659, 10]-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.