Information on Result #712345
Linear OA(5136, 646, F5, 42) (dual of [646, 510, 43]-code), using construction XX applied to C1 = C([116,155]), C2 = C([120,157]), C3 = C1 + C2 = C([120,155]), and C∩ = C1 ∩ C2 = C([116,157]) based on
- linear OA(5126, 624, F5, 40) (dual of [624, 498, 41]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {116,117,…,155}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,157}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(5131, 624, F5, 42) (dual of [624, 493, 43]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {116,117,…,157}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(5114, 624, F5, 36) (dual of [624, 510, 37]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,155}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
- linear OA(51, 6, F5, 1) (dual of [6, 5, 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 OOA(5136, 323, F5, 2, 42) (dual of [(323, 2), 510, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5136, 215, F5, 3, 42) (dual of [(215, 3), 509, 43]-NRT-code) | [i] | ||