Information on Result #835498
Linear OOA(529, 322, F5, 2, 8) (dual of [(322, 2), 615, 9]-NRT-code), using OOA 2-folding based on linear OA(529, 644, F5, 8) (dual of [644, 615, 9]-code), using
- construction XX applied to C1 = C([150,156]), C2 = C([154,157]), C3 = C1 + C2 = C([154,156]), and C∩ = C1 ∩ C2 = C([150,157]) [i] based on
- linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {150,151,…,156}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(513, 624, F5, 4) (dual of [624, 611, 5]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {154,155,156,157}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {150,151,…,157}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(59, 624, F5, 3) (dual of [624, 615, 4]-code or 624-cap in PG(8,5)), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {154,155,156}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(5150, 4194623, F5, 2, 16) (dual of [(4194623, 2), 8389096, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |