Information on Result #1015919
Linear OOA(928, 400, F9, 3, 8) (dual of [(400, 3), 1172, 9]-NRT-code), using (u, u+v)-construction based on
- linear OOA(910, 367, F9, 3, 4) (dual of [(367, 3), 1091, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(910, 734, F9, 4) (dual of [734, 724, 5]-code), using
- construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
- linear OA(97, 728, F9, 3) (dual of [728, 721, 4]-code or 728-cap in PG(6,9)), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(97, 728, F9, 3) (dual of [728, 721, 4]-code or 728-cap in PG(6,9)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(910, 728, F9, 4) (dual of [728, 718, 5]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(94, 728, F9, 2) (dual of [728, 724, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([727,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([727,2]) [i] based on
- OA 2-folding and stacking [i] based on linear OA(910, 734, F9, 4) (dual of [734, 724, 5]-code), using
- linear OOA(918, 200, F9, 3, 8) (dual of [(200, 3), 582, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 18, 200)-net over F9, using
- trace code for nets [i] based on digital (1, 9, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 9, 100)-net over F81, using
- extracting embedded OOA [i] based on digital (10, 18, 200)-net over F9, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(9150, 5592802, F9, 3, 16) (dual of [(5592802, 3), 16778256, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |