Information on Result #944664
Linear OOA(810, 258, F8, 3, 4) (dual of [(258, 3), 764, 5]-NRT-code), using OA 2-folding and stacking based on linear OA(810, 516, F8, 4) (dual of [516, 506, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 517, F8, 4) (dual of [517, 507, 5]-code), using
- construction XX applied to C1 = C([510,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([510,2]) [i] based on
- linear OA(87, 511, F8, 3) (dual of [511, 504, 4]-code or 511-cap in PG(6,8)), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(87, 511, F8, 3) (dual of [511, 504, 4]-code or 511-cap in PG(6,8)), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(810, 511, F8, 4) (dual of [511, 501, 5]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(84, 511, F8, 2) (dual of [511, 507, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([510,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([510,2]) [i] based on
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(868, 5592660, F8, 3, 8) (dual of [(5592660, 3), 16777912, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(876, 5592660, F8, 3, 9) (dual of [(5592660, 3), 16777904, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(810, 258, F8, 4, 4) (dual of [(258, 4), 1022, 5]-NRT-code) | [i] | Appending kth Column | |