Information on Result #710881
Linear OA(541, 644, F5, 12) (dual of [644, 603, 13]-code), using construction XX applied to C1 = C([146,156]), C2 = C([150,157]), C3 = C1 + C2 = C([150,156]), and C∩ = C1 ∩ C2 = C([146,157]) based on
- linear OA(533, 624, F5, 11) (dual of [624, 591, 12]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,156}, and designed minimum distance d ≥ |I|+1 = 12 [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(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,157}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- 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(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(541, 322, F5, 2, 12) (dual of [(322, 2), 603, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(541, 214, F5, 3, 12) (dual of [(214, 3), 601, 13]-NRT-code) | [i] | ||