Information on Result #711814
Linear OA(5108, 649, F5, 33) (dual of [649, 541, 34]-code), using construction XX applied to C1 = C([126,156]), C2 = C([130,158]), C3 = C1 + C2 = C([130,156]), and C∩ = C1 ∩ C2 = C([126,158]) based on
- linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,156}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(591, 624, F5, 29) (dual of [624, 533, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,158}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,158}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {130,131,…,156}, and designed minimum distance d ≥ |I|+1 = 28 [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(5109, 650, F5, 33) (dual of [650, 541, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5108, 324, F5, 2, 33) (dual of [(324, 2), 540, 34]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5108, 216, F5, 3, 33) (dual of [(216, 3), 540, 34]-NRT-code) | [i] | ||