Information on Result #711883
Linear OA(5112, 649, F5, 34) (dual of [649, 537, 35]-code), using construction XX applied to C1 = C([130,161]), C2 = C([128,157]), C3 = C1 + C2 = C([130,157]), and C∩ = C1 ∩ C2 = C([128,161]) based on
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,161}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(595, 624, F5, 30) (dual of [624, 529, 31]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,157}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,161}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(587, 624, F5, 28) (dual of [624, 537, 29]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,157}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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 OA(5113, 650, F5, 34) (dual of [650, 537, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5112, 324, F5, 2, 34) (dual of [(324, 2), 536, 35]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5112, 216, F5, 3, 34) (dual of [(216, 3), 536, 35]-NRT-code) | [i] | ||