Information on Result #711080
Linear OA(561, 644, F5, 18) (dual of [644, 583, 19]-code), using construction XX applied to C1 = C([140,156]), C2 = C([144,157]), C3 = C1 + C2 = C([144,156]), and C∩ = C1 ∩ C2 = C([140,157]) based on
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {140,141,…,156}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {144,145,…,157}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {140,141,…,157}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(541, 624, F5, 13) (dual of [624, 583, 14]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {144,145,…,156}, and designed minimum distance d ≥ |I|+1 = 14 [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(561, 322, F5, 2, 18) (dual of [(322, 2), 583, 19]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(561, 214, F5, 3, 18) (dual of [(214, 3), 581, 19]-NRT-code) | [i] | ||